CINXE.COM

<!DOCTYPE html> <html lang="en" xmlns:fb="http://www.facebook.com/2008/fbml" class="wf-loading"> <head prefix="og: https://ogp.me/ns# fb: https://ogp.me/ns/fb# academia: https://ogp.me/ns/fb/academia#"> <meta charset="utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <title>Konrad Zdanowski - Academia.edu</title>  <link href="//a.academia-assets.com/images/favicons/favicon-production.ico" rel="shortcut icon" type="image/vnd.microsoft.icon"> <link rel="apple-touch-icon" sizes="57x57" href="//a.academia-assets.com/images/favicons/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon" sizes="60x60" href="//a.academia-assets.com/images/favicons/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon" sizes="72x72" href="//a.academia-assets.com/images/favicons/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon" sizes="76x76" href="//a.academia-assets.com/images/favicons/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon" sizes="114x114" href="//a.academia-assets.com/images/favicons/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon" sizes="120x120" href="//a.academia-assets.com/images/favicons/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon" sizes="144x144" href="//a.academia-assets.com/images/favicons/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon" sizes="152x152" href="//a.academia-assets.com/images/favicons/apple-touch-icon-152x152.png"> <link rel="apple-touch-icon" sizes="180x180" href="//a.academia-assets.com/images/favicons/apple-touch-icon-180x180.png"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-194x194.png" sizes="194x194"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/android-chrome-192x192.png" sizes="192x192"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-16x16.png" sizes="16x16"> <link rel="manifest" href="//a.academia-assets.com/images/favicons/manifest.json"> <meta name="msapplication-TileColor" content="#2b5797"> <meta name="msapplication-TileImage" content="//a.academia-assets.com/images/favicons/mstile-144x144.png"> <meta name="theme-color" content="#ffffff"> <script> window.performance && window.performance.measure && window.performance.measure("Time To First Byte", "requestStart", "responseStart"); </script> <script> (function() { if (!window.URLSearchParams || !window.history || !window.history.replaceState) { return; } var searchParams = new URLSearchParams(window.location.search); var paramsToDelete = [ 'fs', 'sm', 'swp', 'iid', 'nbs', 'rcc', // related content category 'rcpos', // related content carousel position 'rcpg', // related carousel page 'rchid', // related content hit id 'f_ri', // research interest id, for SEO tracking 'f_fri', // featured research interest, for SEO tracking (param key without value) 'f_rid', // from research interest directory for SEO tracking 'f_loswp', // from research interest pills on LOSWP sidebar for SEO tracking 'rhid', // referrring hit id ]; if (paramsToDelete.every((key) => searchParams.get(key) === null)) { return; } paramsToDelete.forEach((key) => { searchParams.delete(key); }); var cleanUrl = new URL(window.location.href); cleanUrl.search = searchParams.toString(); history.replaceState({}, document.title, cleanUrl); })(); </script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "profiles/works", 'action': "summary", 'controller_action': 'profiles/works#summary', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script type="text/javascript"> window.sendUserTiming = function(timingName) { if (!(window.performance && window.performance.measure)) return; var entries = window.performance.getEntriesByName(timingName, "measure"); if (entries.length !== 1) return; var timingValue = Math.round(entries[0].duration); gtag('event', 'timing_complete', { name: timingName, value: timingValue, event_category: 'User-centric', }); }; window.sendUserTiming("Time To First Byte"); </script> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="H9ICCQlSOBnq+lr5kBpnUc2ot9vjEtF1oBKPQNTIWMCfefnQEWOlcvAmAeLzbhF4WfdFyuHKK4xeK6RmTN4OeA==" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/wow-77f7b87cb1583fc59aa8f94756ebfe913345937eb932042b4077563bebb5fb4b.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/social/home-9e8218e1301001388038e3fc3427ed00d079a4760ff7745d1ec1b2d59103170a.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/heading-b2b823dd904da60a48fd1bfa1defd840610c2ff414d3f39ed3af46277ab8df3b.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-3cea6e0ad4715ed965c49bfb15dedfc632787b32ff6d8c3a474182b231146ab7.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Gupter:wght@400;500;700&family=IBM+Plex+Mono:wght@300;400&family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-2b6f90dbd75f5941bc38f4ad716615f3ac449e7398313bb3bc225fba451cd9fa.css" /> <meta name="author" content="konrad zdanowski" /> <meta name="description" content="Konrad Zdanowski: 6 Followers, 3 Following, 9 Research papers. Research interests: Epistemic Logic, Computational Complexity, and Theoretical Computer Science." /> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs" /> <script> var $controller_name = 'works'; var $action_name = "summary"; var $rails_env = 'production'; var $app_rev = '48654d67e5106e06fb1e5c9a356c302510d6cfee'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.Aedu = { hit_data: null }; window.Aedu.SiteStats = {"premium_universities_count":15279,"monthly_visitors":"125 million","monthly_visitor_count":125874410,"monthly_visitor_count_in_millions":125,"user_count":279006121,"paper_count":55203019,"paper_count_in_millions":55,"page_count":432000000,"page_count_in_millions":432,"pdf_count":16500000,"pdf_count_in_millions":16}; window.Aedu.serverRenderTime = new Date(1734520607000); window.Aedu.timeDifference = new Date().getTime() - 1734520607000; window.Aedu.isUsingCssV1 = false; window.Aedu.enableLocalization = true; window.Aedu.activateFullstory = false; window.Aedu.serviceAvailability = { status: {"attention_db":"on","bibliography_db":"on","contacts_db":"on","email_db":"on","indexability_db":"on","mentions_db":"on","news_db":"on","notifications_db":"on","offsite_mentions_db":"on","redshift":"on","redshift_exports_db":"on","related_works_db":"on","ring_db":"on","user_tests_db":"on"}, serviceEnabled: function(service) { return this.status[service] === "on"; }, readEnabled: function(service) { return this.serviceEnabled(service) || this.status[service] === "read_only"; }, }; window.Aedu.viewApmTrace = function() { // Check if x-apm-trace-id meta tag is set, and open the trace in APM // in a new window if it is. var apmTraceId = document.head.querySelector('meta[name="x-apm-trace-id"]'); if (apmTraceId) { var traceId = apmTraceId.content; // Use trace ID to construct URL, an example URL looks like: // https://app.datadoghq.com/apm/traces?query=trace_id%31298410148923562634 var apmUrl = 'https://app.datadoghq.com/apm/traces?query=trace_id%3A' + traceId; window.open(apmUrl, '_blank'); } }; </script>  <link href="https://fonts.googleapis.com/css?family=Roboto:100,100i,300,300i,400,400i,500,500i,700,700i,900,900i" rel="stylesheet"> <link href="//maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" rel="stylesheet"> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/libraries-a9675dcb01ec4ef6aa807ba772c7a5a00c1820d3ff661c1038a20f80d06bb4e4.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/academia-0fb6fc03c471832908791ad7ddba619b6165b3ccf7ae0f65cf933f34b0b660a7.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system_legacy-056a9113b9a0f5343d013b29ee1929d5a18be35fdcdceb616600b4db8bd20054.css" /> <script src="//a.academia-assets.com/assets/webpack_bundles/runtime-bundle-005434038af4252ca37c527588411a3d6a0eabb5f727fac83f8bbe7fd88d93bb.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/webpack_libraries_and_infrequently_changed.wjs-bundle-772ddef14990ef25ff745ff7a68e1f5d083987771af2b9046e5dd4ece84c9e02.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/core_webpack.wjs-bundle-8ced32df41cb1a30061eaa13a8fe865a252f94d76a6a6a05ea0ba77c04f53a96.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/sentry.wjs-bundle-5fe03fddca915c8ba0f7edbe64c194308e8ce5abaed7bffe1255ff37549c4808.js"></script> <script> jade = window.jade || {}; jade.helpers = window.$h; jade._ = window._; </script>  <script id="tag-manager-head-root">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer_old','GTM-5G9JF7Z');</script>  <script> window.gptadslots = []; window.googletag = window.googletag || {}; window.googletag.cmd = window.googletag.cmd || []; </script> <script type="text/javascript"> // TODO(jacob): This should be defined, may be rare load order problem. // Checking if null is just a quick fix, will default to en if unset. // Better fix is to run this immedietely after I18n is set. if (window.I18n != null) { I18n.defaultLocale = "en"; I18n.locale = "en"; I18n.fallbacks = true; } </script> <link rel="canonical" href="https://independent.academia.edu/KonradZdanowski" /> </head>   <body class='c-profiles/works a-summary logged_out'>  <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script><script>window.fbAsyncLoad = function() { // Protection against double calling of this function if (window.FB) { return; } (function(d, s, id){ var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) {return;} js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_US/sdk.js"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk')); } if (!window.defer_facebook) { // Autoload if not deferred window.fbAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.fbAsyncLoad(); }, 5000); }</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script><script>window.googleAsyncLoad = function() { // Protection against double calling of this function (function(d) { var js; var id = 'google-jssdk'; var ref = d.getElementsByTagName('script')[0]; if (d.getElementById(id)) { return; } js = d.createElement('script'); js.id = id; js.async = true; js.onload = loadGoogle; js.src = "https://accounts.google.com/gsi/client" ref.parentNode.insertBefore(js, ref); }(document)); } if (!window.defer_google) { // Autoload if not deferred window.googleAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.googleAsyncLoad(); }, 5000); }</script> <div id="tag-manager-body-root">  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-5G9JF7Z" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>   <script> window.addEventListener('load', function() { if (document.querySelector('input[name="commit"]')) { document.querySelector('input[name="commit"]').addEventListener('click', function() { gtag('event', 'click', { event_category: 'button', event_label: 'Log In' }) }) } }); </script> </div> <script>var _comscore = _comscore || []; _comscore.push({ c1: "2", c2: "26766707" }); (function() { var s = document.createElement("script"), el = document.getElementsByTagName("script")[0]; s.async = true; s.src = (document.location.protocol == "https:" ? "https://sb" : "http://b") + ".scorecardresearch.com/beacon.js"; el.parentNode.insertBefore(s, el); })();</script><img src="https://sb.scorecardresearch.com/p?c1=2&c2=26766707&cv=2.0&cj=1" style="position: absolute; visibility: hidden" /> <div id='react-modal'></div> <div class='DesignSystem'> <a class='u-showOnFocus' href='#site'> Skip to main content </a> </div> <div id="upgrade_ie_banner" style="display: none;"><p>Academia.edu no longer supports Internet Explorer.</p><p>To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to <a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.getElementById('upgrade_ie_banner').style.display = 'block'; }</script> <div class="DesignSystem bootstrap ShrinkableNav"><div class="navbar navbar-default main-header"><div class="container-wrapper" id="main-header-container"><div class="container"><div class="navbar-header"><div class="nav-left-wrapper u-mt0x"><div class="nav-logo"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="visible-xs-inline-block" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hidden-xs" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a></div><div class="nav-search"><div class="SiteSearch-wrapper select2-no-default-pills"><form class="js-SiteSearch-form DesignSystem" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><i class="SiteSearch-icon fa fa-search u-fw700 u-positionAbsolute u-tcGrayDark"></i><input class="js-SiteSearch-form-input SiteSearch-form-input form-control" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" value="" /></form></div></div></div><div class="nav-right-wrapper pull-right"><ul class="NavLinks js-main-nav list-unstyled"><li class="NavLinks-link"><a class="js-header-login-url Button Button--inverseGray Button--sm u-mb4x" id="nav_log_in" rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="NavLinks-link u-p0x"><a class="Button Button--inverseGray Button--sm u-mb4x" rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li></ul><button class="hidden-lg hidden-md hidden-sm u-ml4x navbar-toggle collapsed" data-target=".js-mobile-header-links" data-toggle="collapse" type="button"><span class="icon-bar"></span><span class="icon-bar"></span><span class="icon-bar"></span></button></div></div><div class="collapse navbar-collapse js-mobile-header-links"><ul class="nav navbar-nav"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li><li class="u-borderColorGrayLight u-borderBottom1 js-mobile-nav-expand-trigger"><a href="#">more&nbsp<span class="caret"></span></a></li><li><ul class="js-mobile-nav-expand-section nav navbar-nav u-m0x collapse"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/about">About</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/press">Press</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/documents">Papers</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/hiring"><i class="fa fa-briefcase"></i> We're Hiring!</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://support.academia.edu/"><i class="fa fa-question-circle"></i> Help Center</a></li><li class="js-mobile-nav-collapse-trigger u-borderColorGrayLight u-borderBottom1 dropup" style="display:none"><a href="#">less&nbsp<span class="caret"></span></a></li></ul></li></ul></div></div></div><script>(function(){ var $moreLink = $(".js-mobile-nav-expand-trigger"); var $lessLink = $(".js-mobile-nav-collapse-trigger"); var $section = $('.js-mobile-nav-expand-section'); $moreLink.click(function(ev){ ev.preventDefault(); $moreLink.hide(); $lessLink.show(); $section.collapse('show'); }); $lessLink.click(function(ev){ ev.preventDefault(); $moreLink.show(); $lessLink.hide(); $section.collapse('hide'); }); })() if ($a.is_logged_in() || false) { new Aedu.NavigationController({ el: '.js-main-nav', showHighlightedNotification: false }); } else { $(".js-header-login-url").attr("href", $a.loginUrlWithRedirect()); } Aedu.autocompleteSearch = new AutocompleteSearch({el: '.js-SiteSearch-form'});</script></div></div> <div id='site' class='fixed'> <div id="content" class="clearfix"> <script>document.addEventListener('DOMContentLoaded', function(){ var $dismissible = $(".dismissible_banner"); $dismissible.click(function(ev) { $dismissible.hide(); }); });</script> <script src="//a.academia-assets.com/assets/webpack_bundles/profile.wjs-bundle-77c1bbdf640d3ab9a9b87cd905f5a36d6e6aeca610cba7e42bc42af726770bbb.js" defer="defer"></script><script>Aedu.rankings = { showPaperRankingsLink: false } $viewedUser = Aedu.User.set_viewed( {"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski","photo":"/images/s65_no_pic.png","has_photo":false,"is_analytics_public":false,"interests":[{"id":12685,"name":"Epistemic Logic","url":"https://www.academia.edu/Documents/in/Epistemic_Logic"},{"id":2189,"name":"Computational Complexity","url":"https://www.academia.edu/Documents/in/Computational_Complexity"},{"id":17100,"name":"Theoretical Computer Science","url":"https://www.academia.edu/Documents/in/Theoretical_Computer_Science"},{"id":2534,"name":"Multiagent Systems","url":"https://www.academia.edu/Documents/in/Multiagent_Systems"}]} ); if ($a.is_logged_in() && $viewedUser.is_current_user()) { $('body').addClass('profile-viewed-by-owner'); } $socialProfiles = []</script><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/KonradZdanowski","location":"/KonradZdanowski","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/KonradZdanowski","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="ProfileCheckPaperUpdate" data-props="{}" data-trace="false" data-dom-id="ProfileCheckPaperUpdate-react-component-03ec95b4-7c11-459a-b8ae-b135fa06e2fa"></div> <div id="ProfileCheckPaperUpdate-react-component-03ec95b4-7c11-459a-b8ae-b135fa06e2fa"></div> <div class="DesignSystem"><div class="onsite-ping" id="onsite-ping"></div></div><div class="profile-user-info DesignSystem"><div class="social-profile-container"><div class="left-panel-container"><div class="user-info-component-wrapper"><div class="user-summary-cta-container"><div class="user-summary-container"><div class="social-profile-avatar-container"><img class="profile-avatar u-positionAbsolute" border="0" alt="" src="//a.academia-assets.com/images/s200_no_pic.png" /></div><div class="title-container"><h1 class="ds2-5-heading-sans-serif-sm">Konrad Zdanowski</h1><div class="affiliations-container fake-truncate js-profile-affiliations"></div></div></div><div class="sidebar-cta-container"><button class="ds2-5-button hidden profile-cta-button grow js-profile-follow-button" data-broccoli-component="user-info.follow-button" data-click-track="profile-user-info-follow-button" data-follow-user-fname="Konrad" data-follow-user-id="41138865" data-follow-user-source="profile_button" data-has-google="false"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">add</span>Follow</button><button class="ds2-5-button hidden profile-cta-button grow js-profile-unfollow-button" data-broccoli-component="user-info.unfollow-button" data-click-track="profile-user-info-unfollow-button" data-unfollow-user-id="41138865"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">done</span>Following</button></div></div><div class="user-stats-container"><a><div class="stat-container js-profile-followers"><p class="label">Followers</p><p class="data">6</p></div></a><a><div class="stat-container js-profile-followees" data-broccoli-component="user-info.followees-count" data-click-track="profile-expand-user-info-following"><p class="label">Following</p><p class="data">3</p></div></a><a><div class="stat-container js-profile-coauthors" data-broccoli-component="user-info.coauthors-count" data-click-track="profile-expand-user-info-coauthors"><p class="label">Co-authors</p><p class="data">3</p></div></a><span><div class="stat-container"><p class="label"><span class="js-profile-total-view-text">Public Views</span></p><p class="data"><span class="js-profile-view-count"></span></p></div></span></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="41138865" href="https://www.academia.edu/Documents/in/Epistemic_Logic"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://independent.academia.edu/KonradZdanowski","location":"/KonradZdanowski","scheme":"https","host":"independent.academia.edu","port":null,"pathname":"/KonradZdanowski","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Epistemic Logic"]}" data-trace="false" data-dom-id="Pill-react-component-80f9ceb2-2f98-4675-ab25-6231ef5bc63a"></div> <div id="Pill-react-component-80f9ceb2-2f98-4675-ab25-6231ef5bc63a"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="41138865" href="https://www.academia.edu/Documents/in/Computational_Complexity"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Computational Complexity"]}" data-trace="false" data-dom-id="Pill-react-component-2fcacb3c-4d6c-4548-80bf-ecb43bc79cfa"></div> <div id="Pill-react-component-2fcacb3c-4d6c-4548-80bf-ecb43bc79cfa"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="41138865" href="https://www.academia.edu/Documents/in/Theoretical_Computer_Science"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Theoretical Computer Science"]}" data-trace="false" data-dom-id="Pill-react-component-af37432d-bd7d-4839-9ac5-3f5e05693599"></div> <div id="Pill-react-component-af37432d-bd7d-4839-9ac5-3f5e05693599"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="41138865" href="https://www.academia.edu/Documents/in/Multiagent_Systems"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Multiagent Systems"]}" data-trace="false" data-dom-id="Pill-react-component-57b1214a-d4a6-4c0c-91c7-2925a9685b32"></div> <div id="Pill-react-component-57b1214a-d4a6-4c0c-91c7-2925a9685b32"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Konrad Zdanowski</h3></div><div class="js-work-strip profile--work_container" data-work-id="30409290"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic"><img alt="Research paper thumbnail of On the Mints Hierarchy in First-Order Intuitionistic Logic" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic">On the Mints Hierarchy in First-Order Intuitionistic Logic</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://mimuw.academia.edu/AleksySchubert">Aleksy Schubert</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30409290"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30409290"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30409290; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30409290]").text(description); $(".js-view-count[data-work-id=30409290]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30409290; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30409290']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30409290, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=30409290]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30409290,"title":"On the Mints Hierarchy in First-Order Intuitionistic Logic","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":null,"internal_url":"https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic","translated_internal_url":"","created_at":"2016-12-12T14:54:20.524-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":1232838,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26552504,"work_id":30409290,"tagging_user_id":1232838,"tagged_user_id":41138865,"co_author_invite_id":null,"email":"k***i@gmail.com","display_order":0,"name":"Konrad Zdanowski","title":"On the Mints Hierarchy in First-Order Intuitionistic Logic"},{"id":26552535,"work_id":30409290,"tagging_user_id":1232838,"tagged_user_id":null,"co_author_invite_id":2211378,"email":"u***y@mimuw.edu.pl","display_order":4194304,"name":"Paweł Urzyczyn","title":"On the Mints Hierarchy in First-Order Intuitionistic Logic"}],"downloadable_attachments":[],"slug":"On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":null,"owner":{"id":1232838,"first_name":"Aleksy","middle_initials":"","last_name":"Schubert","page_name":"AleksySchubert","domain_name":"mimuw","created_at":"2012-02-22T05:26:30.159-08:00","display_name":"Aleksy Schubert","url":"https://mimuw.academia.edu/AleksySchubert"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105216"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105216/Finite_Arithmetics"><img alt="Research paper thumbnail of Finite Arithmetics" class="work-thumbnail" src="https://attachments.academia-assets.com/41990674/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105216/Finite_Arithmetics">Finite Arithmetics</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Fundamenta Informaticae</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The paper presents the current state of knowledge in the field of logical investigations of finit...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="aa39b23ed442421f339851c7192eee51" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41990674,"asset_id":20105216,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105216"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105216"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105216; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105216]").text(description); $(".js-view-count[data-work-id=20105216]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105216; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105216']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105216, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "aa39b23ed442421f339851c7192eee51" } } $('.js-work-strip[data-work-id=20105216]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105216,"title":"Finite Arithmetics","translated_title":"","metadata":{"abstract":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","publication_name":"Fundamenta Informaticae"},"translated_abstract":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","internal_url":"https://www.academia.edu/20105216/Finite_Arithmetics","translated_internal_url":"","created_at":"2016-01-08T08:14:00.198-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710311,"work_id":20105216,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Finite Arithmetics"},{"id":12710313,"work_id":20105216,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":4194304,"name":"Michał Krynicki","title":"Finite Arithmetics"}],"downloadable_attachments":[{"id":41990674,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41990674/thumbnails/1.jpg","file_name":"Finite_Arithmetics20160203-17182-17raqzi.pdf","download_url":"https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Finite_Arithmetics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41990674/Finite_Arithmetics20160203-17182-17raqzi-libre.pdf?1454542449=\u0026response-content-disposition=attachment%3B+filename%3DFinite_Arithmetics.pdf\u0026Expires=1734524206\u0026Signature=WqPx5gmKNzu94-NHiVF7IIvB-opEiyEyQ-I6rvURcJQCUXF68gP8iOFcWAXz3fQoPeXhjRWuiCGZfr1mUND1oSX7KaMV7A0p5ZiJOisHBIC-Xpi~P9yR8ALAMZnElEylGXnwcPRpAmvi2Wm6dXBvDxCYjA3Gx9ruqffoqdvyLTIWJzZ6H7DcjGCUyYSPhVm3FlCcA0O1Os1~IRfyvLDdauAvSfjTVltJJOk2SO23tuW0qZmnVBJ-EUJHQuwGCMmlrCy7YKt5rEdocwempTseC0DeupJkjFsnmHtYog~4mB7XukaxCuJiIFWkrX9B6nL4TezQ548ZiHSBISZ1YJjHRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Finite_Arithmetics","translated_slug":"","page_count":22,"language":"en","content_type":"Work","summary":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41990674,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41990674/thumbnails/1.jpg","file_name":"Finite_Arithmetics20160203-17182-17raqzi.pdf","download_url":"https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Finite_Arithmetics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41990674/Finite_Arithmetics20160203-17182-17raqzi-libre.pdf?1454542449=\u0026response-content-disposition=attachment%3B+filename%3DFinite_Arithmetics.pdf\u0026Expires=1734524206\u0026Signature=WqPx5gmKNzu94-NHiVF7IIvB-opEiyEyQ-I6rvURcJQCUXF68gP8iOFcWAXz3fQoPeXhjRWuiCGZfr1mUND1oSX7KaMV7A0p5ZiJOisHBIC-Xpi~P9yR8ALAMZnElEylGXnwcPRpAmvi2Wm6dXBvDxCYjA3Gx9ruqffoqdvyLTIWJzZ6H7DcjGCUyYSPhVm3FlCcA0O1Os1~IRfyvLDdauAvSfjTVltJJOk2SO23tuW0qZmnVBJ-EUJHQuwGCMmlrCy7YKt5rEdocwempTseC0DeupJkjFsnmHtYog~4mB7XukaxCuJiIFWkrX9B6nL4TezQ548ZiHSBISZ1YJjHRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":6353663,"url":"https://www.researchgate.net/profile/Marcin_Mostowski/publication/220444508_Finite_Arithmetics/links/0912f5100379943365000000.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105215"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata"><img alt="Research paper thumbnail of A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata" class="work-thumbnail" src="https://attachments.academia-assets.com/41164273/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata">A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ad4755fe8ced6b616b4a206fb83c9294" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164273,"asset_id":20105215,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105215"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105215"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105215; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105215]").text(description); $(".js-view-count[data-work-id=20105215]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105215; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105215']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105215, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ad4755fe8ced6b616b4a206fb83c9294" } } $('.js-work-strip[data-work-id=20105215]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105215,"title":"A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata","translated_internal_url":"","created_at":"2016-01-08T08:14:00.052-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710314,"work_id":20105215,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2983265,"email":"t***t@laposte.net","display_order":0,"name":"Thomas Colcombet","title":"A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata"}],"downloadable_attachments":[{"id":41164273,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164273/thumbnails/1.jpg","file_name":"A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207.pdf","download_url":"https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Tight_Lower_Bound_for_Determinization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164273/A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207-libre.pdf?1452836895=\u0026response-content-disposition=attachment%3B+filename%3DA_Tight_Lower_Bound_for_Determinization.pdf\u0026Expires=1734524206\u0026Signature=gV5k1bnSCGdNlETBZvDYMeAb99d4nFUmDrFzIlaYlfjXAdkrriwif-1Dsg8gA4cQSedndMBiRcs5VBjGqRV8DvUmfW3OkJbYV0FXXLpEqUxQntWKNkbqOWwiNbEK3Pkg-BibrwdtpKQTJ5A0FJv0qo5E40MIZ24GST81AjeiHa4iMAKkb8Uvfby2yrgEIft8FcVwJE4fJvNgR08RjFM0srne~W6FhRiK2sF2vpyjw5VHmcU9KmeVXQVFt0ZKC~t6KXbu~tRys~raeXbI8R7Lr6afOHLFUxvGEzsiaAAr1jjUkCnmJ1At2eaOY79YpTrdiUcQUjD3UuEH-Cu4wm1BMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_Büchi_Automata","translated_slug":"","page_count":59,"language":"en","content_type":"Work","summary":null,"owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164273,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164273/thumbnails/1.jpg","file_name":"A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207.pdf","download_url":"https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Tight_Lower_Bound_for_Determinization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164273/A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207-libre.pdf?1452836895=\u0026response-content-disposition=attachment%3B+filename%3DA_Tight_Lower_Bound_for_Determinization.pdf\u0026Expires=1734524206\u0026Signature=gV5k1bnSCGdNlETBZvDYMeAb99d4nFUmDrFzIlaYlfjXAdkrriwif-1Dsg8gA4cQSedndMBiRcs5VBjGqRV8DvUmfW3OkJbYV0FXXLpEqUxQntWKNkbqOWwiNbEK3Pkg-BibrwdtpKQTJ5A0FJv0qo5E40MIZ24GST81AjeiHa4iMAKkb8Uvfby2yrgEIft8FcVwJE4fJvNgR08RjFM0srne~W6FhRiK2sF2vpyjw5VHmcU9KmeVXQVFt0ZKC~t6KXbu~tRys~raeXbI8R7Lr6afOHLFUxvGEzsiaAAr1jjUkCnmJ1At2eaOY79YpTrdiUcQUjD3UuEH-Cu4wm1BMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":571143,"name":"Lower Bound","url":"https://www.academia.edu/Documents/in/Lower_Bound"},{"id":575846,"name":"Upper Bound","url":"https://www.academia.edu/Documents/in/Upper_Bound"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105214"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105214/FM_Representability_and_Beyond"><img alt="Research paper thumbnail of FM-Representability and Beyond" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105214/FM_Representability_and_Beyond">FM-Representability and Beyond</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\Sigma_{\rm 2}^{\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\Sigma_{\rm 2}^{\rm 0}–complete and that the set of formulae FM–representing some relations is P03\Pi^{0}_{3}–complete.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105214"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105214"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105214; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105214]").text(description); $(".js-view-count[data-work-id=20105214]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105214; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105214']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105214, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20105214]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105214,"title":"FM-Representability and Beyond","translated_title":"","metadata":{"abstract":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","internal_url":"https://www.academia.edu/20105214/FM_Representability_and_Beyond","translated_internal_url":"","created_at":"2016-01-08T08:13:59.927-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710310,"work_id":20105214,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"FM-Representability and Beyond"}],"downloadable_attachments":[],"slug":"FM_Representability_and_Beyond","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105213"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105213/Coprimality_in_Finite_Models"><img alt="Research paper thumbnail of Coprimality in Finite Models" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105213/Coprimality_in_Finite_Models">Coprimality in Finite Models</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We investigate properties of the coprimality relation within the family of finite models...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\mathrm{FM}((\omega,\bot)). Within FM((w,^))\mathrm{FM}((\omega,\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\mathrm{FM}((\omega,\bot)) is Π01^{\rm 0}_{\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\omega,\bot,\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\omega,\bot,\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\omega,\bot,\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105213"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105213"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105213; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105213]").text(description); $(".js-view-count[data-work-id=20105213]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105213; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105213']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105213, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20105213]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105213,"title":"Coprimality in Finite Models","translated_title":"","metadata":{"abstract":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","internal_url":"https://www.academia.edu/20105213/Coprimality_in_Finite_Models","translated_internal_url":"","created_at":"2016-01-08T08:13:59.810-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710308,"work_id":20105213,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Coprimality in Finite Models"}],"downloadable_attachments":[],"slug":"Coprimality_in_Finite_Models","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[],"research_interests":[{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"},{"id":181847,"name":"First-Order Logic","url":"https://www.academia.edu/Documents/in/First-Order_Logic"},{"id":1646429,"name":"Prime Number","url":"https://www.academia.edu/Documents/in/Prime_Number"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105212"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models"><img alt="Research paper thumbnail of Theories of arithmetics in finite models" class="work-thumbnail" src="https://attachments.academia-assets.com/41164160/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models">Theories of arithmetics in finite models</a></div><div class="wp-workCard_item"><span>The Journal of Symbolic Logic</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate theories of initial segments of the standard models for arithmetics. It is easy to...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="11721e9f6321bae3ec77fa50b2531eac" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164160,"asset_id":20105212,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105212"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105212"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105212; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105212]").text(description); $(".js-view-count[data-work-id=20105212]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105212; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105212']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105212, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "11721e9f6321bae3ec77fa50b2531eac" } } $('.js-work-strip[data-work-id=20105212]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105212,"title":"Theories of arithmetics in finite models","translated_title":"","metadata":{"grobid_abstract":"We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"The Journal of Symbolic Logic","grobid_abstract_attachment_id":41164160},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models","translated_internal_url":"","created_at":"2016-01-08T08:13:59.694-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710312,"work_id":20105212,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":0,"name":"Michał Krynicki","title":"Theories of arithmetics in finite models"}],"downloadable_attachments":[{"id":41164160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164160/thumbnails/1.jpg","file_name":"Theories_of_arithmetics_in_finite_models20160114-3921-12h02af.pdf","download_url":"https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_arithmetics_in_finite_models.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164160/Theories_of_arithmetics_in_finite_models20160114-3921-12h02af-libre.pdf?1452836903=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_arithmetics_in_finite_models.pdf\u0026Expires=1734524206\u0026Signature=QoSFYkavDqQ6QYMhsqO6VFM3qh-tFd~bcFM0V4NNwXW8-cjBFMjoqv2Ra3KE4ixRa4LxG~hu9H7ZSCezkhxRud3oPhs5a5wJX2zzBPtNP3PK8n1KkDDHTy14HFwxRCKDKoMkHs8hooHaLcKgP9o6tQ4vWQecq4aEvvkb7vj8hC8glM7FEs81~GHzHWW55w~is8laEduYiLK27e~7yPm8I3oyTYPMMi9AQ6oO5Va9XOaELVSMmvmT2AeuvGxb3rFpyGOZw1iY39LIr6RLHEfncH7qigNWJn8gvENbSraetCuimlGzDaR1jszyludBXfONoBRHyAI5AR0rzq-5O0DtXA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theories_of_arithmetics_in_finite_models","translated_slug":"","page_count":30,"language":"en","content_type":"Work","summary":"We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164160/thumbnails/1.jpg","file_name":"Theories_of_arithmetics_in_finite_models20160114-3921-12h02af.pdf","download_url":"https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_arithmetics_in_finite_models.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164160/Theories_of_arithmetics_in_finite_models20160114-3921-12h02af-libre.pdf?1452836903=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_arithmetics_in_finite_models.pdf\u0026Expires=1734524207\u0026Signature=LOD9RedfQRPL~DO~-kKpNe5cmPr~hY2pOxV6wLUzi~T04mzOYShQ~FlLWivGs3RsW3Mi86S~NhToq7dYNny7cVVe9qzaU-TKLeFyOQGljUCHqOkMGA4MsUyp0GC3~eqkWL7Xe8Q4WNK6JeFwf1CG4kH8FaQBHZFrs55WcZQzHGlQn-V0x59uoKIg6l-U54yiJFvb~fyPktM7MhlSsFLEBgVSfSBVMWErGHxyDNMifQTI4zKHg~hVfaeicTsdPItsXubaHD1u4Fax-Cyoul6A0EegW3JKZnl-bn9095PpQl7eAEPjzlQvw8eQMCK39p8f3ROfMQPHbfwaIWodbCEIfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy"},{"id":8367,"name":"Complexity","url":"https://www.academia.edu/Documents/in/Complexity"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"},{"id":131903,"name":"Arithmetic","url":"https://www.academia.edu/Documents/in/Arithmetic"},{"id":179292,"name":"Symbolic Logic","url":"https://www.academia.edu/Documents/in/Symbolic_Logic"},{"id":321836,"name":"Spectrum","url":"https://www.academia.edu/Documents/in/Spectrum"},{"id":1264826,"name":"Exponential Function","url":"https://www.academia.edu/Documents/in/Exponential_Function"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105211"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann"><img alt="Research paper thumbnail of On a question of Andreas Weiermann" class="work-thumbnail" src="https://attachments.academia-assets.com/41164131/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann">On a question of Andreas Weiermann</a></div><div class="wp-workCard_item"><span>MLQ</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7a55e3b847a8e8aec2d57eb2e3d657d6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164131,"asset_id":20105211,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105211"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105211"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105211; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105211]").text(description); $(".js-view-count[data-work-id=20105211]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105211; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105211']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105211, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7a55e3b847a8e8aec2d57eb2e3d657d6" } } $('.js-work-strip[data-work-id=20105211]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105211,"title":"On a question of Andreas Weiermann","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"MLQ"},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann","translated_internal_url":"","created_at":"2016-01-08T08:13:59.570-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710315,"work_id":20105211,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2983266,"email":"h***i@impan.gov.pl","display_order":0,"name":"Henryk Kotlarski","title":"On a question of Andreas Weiermann"}],"downloadable_attachments":[{"id":41164131,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164131/thumbnails/1.jpg","file_name":"On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns.pdf","download_url":"https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_a_question_of_Andreas_Weiermann.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164131/On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns-libre.pdf?1452836904=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_question_of_Andreas_Weiermann.pdf\u0026Expires=1734524207\u0026Signature=PanJmzVU4pXVRdCB3TGzHpLxljYfJZT5H3kZpBYnZuhVajjiUeh3KMvVoJywLDzK-VRqtCAAZzHAYkmp4TUhM6g5fIjWpD4RVerMXHjPA05GWykxPVf30abAn23oq9UBmqQW9X~HEHriTJrpxdIBUIoBGIR7zl~CbbUjAs-J8v9Ak5ADVBw-3ikE4VJCZJrRBQynrMuUyulr-69mZl2wDEcl4iO4z7EdbYpeSeuhZ6n3-MdSYd5WtTMpuWh4BBzI7DcLEkpPauffIkwqO~aHWxyupclns-nage0msjUDazbNFIQW29JDu7zkKz6kRMq5jdW18icRmJge5eHZ9pr9gQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_a_question_of_Andreas_Weiermann","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":null,"owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164131,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164131/thumbnails/1.jpg","file_name":"On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns.pdf","download_url":"https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_a_question_of_Andreas_Weiermann.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164131/On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns-libre.pdf?1452836904=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_question_of_Andreas_Weiermann.pdf\u0026Expires=1734524207\u0026Signature=PanJmzVU4pXVRdCB3TGzHpLxljYfJZT5H3kZpBYnZuhVajjiUeh3KMvVoJywLDzK-VRqtCAAZzHAYkmp4TUhM6g5fIjWpD4RVerMXHjPA05GWykxPVf30abAn23oq9UBmqQW9X~HEHriTJrpxdIBUIoBGIR7zl~CbbUjAs-J8v9Ak5ADVBw-3ikE4VJCZJrRBQynrMuUyulr-69mZl2wDEcl4iO4z7EdbYpeSeuhZ6n3-MdSYd5WtTMpuWh4BBzI7DcLEkpPauffIkwqO~aHWxyupclns-nage0msjUDazbNFIQW29JDu7zkKz6kRMq5jdW18icRmJge5eHZ9pr9gQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":1190945,"name":"MLQ","url":"https://www.academia.edu/Documents/in/MLQ"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105210"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies"><img alt="Research paper thumbnail of Degrees of logics with Henkin quantifiers in poor vocabularies" class="work-thumbnail" src="https://attachments.academia-assets.com/41164327/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies">Degrees of logics with Henkin quantifiers in poor vocabularies</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Archive for Mathematical Logic</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c38b9dc8089991c04920d28d8af73ef3" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164327,"asset_id":20105210,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105210"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105210"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105210; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105210]").text(description); $(".js-view-count[data-work-id=20105210]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105210; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105210']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105210, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c38b9dc8089991c04920d28d8af73ef3" } } $('.js-work-strip[data-work-id=20105210]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105210,"title":"Degrees of logics with Henkin quantifiers in poor vocabularies","translated_title":"","metadata":{"grobid_abstract":"We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).","publication_date":{"day":null,"month":null,"year":2004,"errors":{}},"publication_name":"Archive for Mathematical Logic","grobid_abstract_attachment_id":41164327},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies","translated_internal_url":"","created_at":"2016-01-08T08:13:59.444-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710309,"work_id":20105210,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Degrees of logics with Henkin quantifiers in poor vocabularies"}],"downloadable_attachments":[{"id":41164327,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164327/thumbnails/1.jpg","file_name":"Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn.pdf","download_url":"https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Degrees_of_logics_with_Henkin_quantifier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164327/Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn-libre.pdf?1452836971=\u0026response-content-disposition=attachment%3B+filename%3DDegrees_of_logics_with_Henkin_quantifier.pdf\u0026Expires=1734524207\u0026Signature=O7WbfADYBG~3HEXrAdtIn-2ouKl1Y2gB6TlQU~iU5cPxw0sADlZIXKvLA0E0afrfpz0yzCKFDFdCi0KDsqtbHLSLW8lTTPGMOOe9dAPRipDbwk-6DWnKSu8kgle636bBwHOeDCs5rktMl9whRGrvUa7v6iI73kskW0TwkK8VaTmAfflcdOMJkz4Yy6PsUGb0sdnz3KOcfxVDfayrsgEL1izbE7qs9jXn0W6Fco-X9sGAX-HuGhjYzfkosdsGLXK-8pdgW46mW0~ZPb-hMDA6sgfSAVRYCCMZZ1OTS0SxQ9iEtd2e-RyzK~pC0RIT4sWL5kDR51sUyvYNjaS-8EZclw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164327,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164327/thumbnails/1.jpg","file_name":"Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn.pdf","download_url":"https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Degrees_of_logics_with_Henkin_quantifier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164327/Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn-libre.pdf?1452836971=\u0026response-content-disposition=attachment%3B+filename%3DDegrees_of_logics_with_Henkin_quantifier.pdf\u0026Expires=1734524207\u0026Signature=O7WbfADYBG~3HEXrAdtIn-2ouKl1Y2gB6TlQU~iU5cPxw0sADlZIXKvLA0E0afrfpz0yzCKFDFdCi0KDsqtbHLSLW8lTTPGMOOe9dAPRipDbwk-6DWnKSu8kgle636bBwHOeDCs5rktMl9whRGrvUa7v6iI73kskW0TwkK8VaTmAfflcdOMJkz4Yy6PsUGb0sdnz3KOcfxVDfayrsgEL1izbE7qs9jXn0W6Fco-X9sGAX-HuGhjYzfkosdsGLXK-8pdgW46mW0~ZPb-hMDA6sgfSAVRYCCMZZ1OTS0SxQ9iEtd2e-RyzK~pC0RIT4sWL5kDR51sUyvYNjaS-8EZclw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":363,"name":"Set Theory","url":"https://www.academia.edu/Documents/in/Set_Theory"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="19973951"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions"><img alt="Research paper thumbnail of Theories of initial segments of standard models of arithmetics and their complete extensions" class="work-thumbnail" src="https://attachments.academia-assets.com/41270357/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions">Theories of initial segments of standard models of arithmetics and their complete extensions</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://u-clermont1.academia.edu/JerzyTomasik">Jerzy Tomasik</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a></span></div><div class="wp-workCard_item"><span>Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate families of finite initial segments of standard models for various arithmetics. We...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="55bdb4850fa5d742fb52c184c457792b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41270357,"asset_id":19973951,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="19973951"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="19973951"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 19973951; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=19973951]").text(description); $(".js-view-count[data-work-id=19973951]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 19973951; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='19973951']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 19973951, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "55bdb4850fa5d742fb52c184c457792b" } } $('.js-work-strip[data-work-id=19973951]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":19973951,"title":"Theories of initial segments of standard models of arithmetics and their complete extensions","translated_title":"","metadata":{"grobid_abstract":"We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.","publication_date":{"day":null,"month":null,"year":2011,"errors":{}},"publication_name":"Theoretical Computer Science","grobid_abstract_attachment_id":41270357},"translated_abstract":null,"internal_url":"https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions","translated_internal_url":"","created_at":"2016-01-02T23:18:38.608-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":40854177,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12457138,"work_id":19973951,"tagging_user_id":40854177,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":0,"name":"Michał Krynicki","title":"Theories of initial segments of standard models of arithmetics and their complete extensions"},{"id":12457140,"work_id":19973951,"tagging_user_id":40854177,"tagged_user_id":41138865,"co_author_invite_id":2924721,"email":"k***i@gmail.com","display_order":4194304,"name":"Konrad Zdanowski","title":"Theories of initial segments of standard models of arithmetics and their complete extensions"}],"downloadable_attachments":[{"id":41270357,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41270357/thumbnails/1.jpg","file_name":"Theories_of_initial_segments_of_standard20160116-28334-wmdyzb.pdf","download_url":"https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_initial_segments_of_standard.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41270357/Theories_of_initial_segments_of_standard20160116-28334-wmdyzb-libre.pdf?1452961467=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_initial_segments_of_standard.pdf\u0026Expires=1734524207\u0026Signature=Qv4dVnLRTtsmj2PkGbD6mBekAyoloxyojX0AEnIJIJ8NindsC6g7eRpmpHyK6UDWl8LzwB8M~Xvm9I~E6QpZD5BxDw3YKw8~12QNUqUmKhweYfew4nUFJU2UXm1177VoMKt8EeyM9mnAHsTeeKkroRtsU3j~zTawzcwK~cuYf8GfnpgNsJYGObAJfScH981~Oxtewhmzw5WEcyhIyz-reSHZlHz23vBUjoXrWUI-FhHGqD~X~hpyfgjt-k~sbYLzANZMQXSaWNi7ejSFeTK9-gMNRf0PhcrU-PFfnjZYW9F~5CjQkoSGfVMQvLhruHhOUrsejh1hGcpB3LQjWuONQw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.","owner":{"id":40854177,"first_name":"Jerzy","middle_initials":null,"last_name":"Tomasik","page_name":"JerzyTomasik","domain_name":"u-clermont1","created_at":"2016-01-02T23:17:53.746-08:00","display_name":"Jerzy Tomasik","url":"https://u-clermont1.academia.edu/JerzyTomasik"},"attachments":[{"id":41270357,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41270357/thumbnails/1.jpg","file_name":"Theories_of_initial_segments_of_standard20160116-28334-wmdyzb.pdf","download_url":"https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_initial_segments_of_standard.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41270357/Theories_of_initial_segments_of_standard20160116-28334-wmdyzb-libre.pdf?1452961467=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_initial_segments_of_standard.pdf\u0026Expires=1734524207\u0026Signature=Qv4dVnLRTtsmj2PkGbD6mBekAyoloxyojX0AEnIJIJ8NindsC6g7eRpmpHyK6UDWl8LzwB8M~Xvm9I~E6QpZD5BxDw3YKw8~12QNUqUmKhweYfew4nUFJU2UXm1177VoMKt8EeyM9mnAHsTeeKkroRtsU3j~zTawzcwK~cuYf8GfnpgNsJYGObAJfScH981~Oxtewhmzw5WEcyhIyz-reSHZlHz23vBUjoXrWUI-FhHGqD~X~hpyfgjt-k~sbYLzANZMQXSaWNi7ejSFeTK9-gMNRf0PhcrU-PFfnjZYW9F~5CjQkoSGfVMQvLhruHhOUrsejh1hGcpB3LQjWuONQw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":17100,"name":"Theoretical Computer Science","url":"https://www.academia.edu/Documents/in/Theoretical_Computer_Science"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="4371504" id="papers"><div class="js-work-strip profile--work_container" data-work-id="30409290"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic"><img alt="Research paper thumbnail of On the Mints Hierarchy in First-Order Intuitionistic Logic" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic">On the Mints Hierarchy in First-Order Intuitionistic Logic</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://mimuw.academia.edu/AleksySchubert">Aleksy Schubert</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2015</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="30409290"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="30409290"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30409290; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30409290]").text(description); $(".js-view-count[data-work-id=30409290]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 30409290; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='30409290']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 30409290, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=30409290]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":30409290,"title":"On the Mints Hierarchy in First-Order Intuitionistic Logic","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":null,"internal_url":"https://www.academia.edu/30409290/On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic","translated_internal_url":"","created_at":"2016-12-12T14:54:20.524-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":1232838,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":26552504,"work_id":30409290,"tagging_user_id":1232838,"tagged_user_id":41138865,"co_author_invite_id":null,"email":"k***i@gmail.com","display_order":0,"name":"Konrad Zdanowski","title":"On the Mints Hierarchy in First-Order Intuitionistic Logic"},{"id":26552535,"work_id":30409290,"tagging_user_id":1232838,"tagged_user_id":null,"co_author_invite_id":2211378,"email":"u***y@mimuw.edu.pl","display_order":4194304,"name":"Paweł Urzyczyn","title":"On the Mints Hierarchy in First-Order Intuitionistic Logic"}],"downloadable_attachments":[],"slug":"On_the_Mints_Hierarchy_in_First_Order_Intuitionistic_Logic","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":null,"owner":{"id":1232838,"first_name":"Aleksy","middle_initials":"","last_name":"Schubert","page_name":"AleksySchubert","domain_name":"mimuw","created_at":"2012-02-22T05:26:30.159-08:00","display_name":"Aleksy Schubert","url":"https://mimuw.academia.edu/AleksySchubert"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105216"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105216/Finite_Arithmetics"><img alt="Research paper thumbnail of Finite Arithmetics" class="work-thumbnail" src="https://attachments.academia-assets.com/41990674/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105216/Finite_Arithmetics">Finite Arithmetics</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Fundamenta Informaticae</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The paper presents the current state of knowledge in the field of logical investigations of finit...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="aa39b23ed442421f339851c7192eee51" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41990674,"asset_id":20105216,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105216"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105216"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105216; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105216]").text(description); $(".js-view-count[data-work-id=20105216]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105216; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105216']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105216, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "aa39b23ed442421f339851c7192eee51" } } $('.js-work-strip[data-work-id=20105216]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105216,"title":"Finite Arithmetics","translated_title":"","metadata":{"abstract":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","publication_name":"Fundamenta Informaticae"},"translated_abstract":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","internal_url":"https://www.academia.edu/20105216/Finite_Arithmetics","translated_internal_url":"","created_at":"2016-01-08T08:14:00.198-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710311,"work_id":20105216,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Finite Arithmetics"},{"id":12710313,"work_id":20105216,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":4194304,"name":"Michał Krynicki","title":"Finite Arithmetics"}],"downloadable_attachments":[{"id":41990674,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41990674/thumbnails/1.jpg","file_name":"Finite_Arithmetics20160203-17182-17raqzi.pdf","download_url":"https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Finite_Arithmetics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41990674/Finite_Arithmetics20160203-17182-17raqzi-libre.pdf?1454542449=\u0026response-content-disposition=attachment%3B+filename%3DFinite_Arithmetics.pdf\u0026Expires=1734524206\u0026Signature=WqPx5gmKNzu94-NHiVF7IIvB-opEiyEyQ-I6rvURcJQCUXF68gP8iOFcWAXz3fQoPeXhjRWuiCGZfr1mUND1oSX7KaMV7A0p5ZiJOisHBIC-Xpi~P9yR8ALAMZnElEylGXnwcPRpAmvi2Wm6dXBvDxCYjA3Gx9ruqffoqdvyLTIWJzZ6H7DcjGCUyYSPhVm3FlCcA0O1Os1~IRfyvLDdauAvSfjTVltJJOk2SO23tuW0qZmnVBJ-EUJHQuwGCMmlrCy7YKt5rEdocwempTseC0DeupJkjFsnmHtYog~4mB7XukaxCuJiIFWkrX9B6nL4TezQ548ZiHSBISZ1YJjHRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Finite_Arithmetics","translated_slug":"","page_count":22,"language":"en","content_type":"Work","summary":"The paper presents the current state of knowledge in the field of logical investigations of finite arithmetics. This is an attempt to summarize the ideas and results in this area. Some new results are presented - these are mainly generalizations of the earlier results related to properties of sl-theories and some nontrivial cases of FM-representability theorem.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41990674,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41990674/thumbnails/1.jpg","file_name":"Finite_Arithmetics20160203-17182-17raqzi.pdf","download_url":"https://www.academia.edu/attachments/41990674/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Finite_Arithmetics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41990674/Finite_Arithmetics20160203-17182-17raqzi-libre.pdf?1454542449=\u0026response-content-disposition=attachment%3B+filename%3DFinite_Arithmetics.pdf\u0026Expires=1734524206\u0026Signature=WqPx5gmKNzu94-NHiVF7IIvB-opEiyEyQ-I6rvURcJQCUXF68gP8iOFcWAXz3fQoPeXhjRWuiCGZfr1mUND1oSX7KaMV7A0p5ZiJOisHBIC-Xpi~P9yR8ALAMZnElEylGXnwcPRpAmvi2Wm6dXBvDxCYjA3Gx9ruqffoqdvyLTIWJzZ6H7DcjGCUyYSPhVm3FlCcA0O1Os1~IRfyvLDdauAvSfjTVltJJOk2SO23tuW0qZmnVBJ-EUJHQuwGCMmlrCy7YKt5rEdocwempTseC0DeupJkjFsnmHtYog~4mB7XukaxCuJiIFWkrX9B6nL4TezQ548ZiHSBISZ1YJjHRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":6353663,"url":"https://www.researchgate.net/profile/Marcin_Mostowski/publication/220444508_Finite_Arithmetics/links/0912f5100379943365000000.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105215"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata"><img alt="Research paper thumbnail of A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata" class="work-thumbnail" src="https://attachments.academia-assets.com/41164273/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata">A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata</a></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ad4755fe8ced6b616b4a206fb83c9294" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164273,"asset_id":20105215,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105215"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105215"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105215; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105215]").text(description); $(".js-view-count[data-work-id=20105215]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105215; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105215']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105215, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ad4755fe8ced6b616b4a206fb83c9294" } } $('.js-work-strip[data-work-id=20105215]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105215,"title":"A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105215/A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_B%C3%BCchi_Automata","translated_internal_url":"","created_at":"2016-01-08T08:14:00.052-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710314,"work_id":20105215,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2983265,"email":"t***t@laposte.net","display_order":0,"name":"Thomas Colcombet","title":"A Tight Lower Bound for Determinization of Transition Labeled Büchi Automata"}],"downloadable_attachments":[{"id":41164273,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164273/thumbnails/1.jpg","file_name":"A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207.pdf","download_url":"https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Tight_Lower_Bound_for_Determinization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164273/A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207-libre.pdf?1452836895=\u0026response-content-disposition=attachment%3B+filename%3DA_Tight_Lower_Bound_for_Determinization.pdf\u0026Expires=1734524206\u0026Signature=gV5k1bnSCGdNlETBZvDYMeAb99d4nFUmDrFzIlaYlfjXAdkrriwif-1Dsg8gA4cQSedndMBiRcs5VBjGqRV8DvUmfW3OkJbYV0FXXLpEqUxQntWKNkbqOWwiNbEK3Pkg-BibrwdtpKQTJ5A0FJv0qo5E40MIZ24GST81AjeiHa4iMAKkb8Uvfby2yrgEIft8FcVwJE4fJvNgR08RjFM0srne~W6FhRiK2sF2vpyjw5VHmcU9KmeVXQVFt0ZKC~t6KXbu~tRys~raeXbI8R7Lr6afOHLFUxvGEzsiaAAr1jjUkCnmJ1At2eaOY79YpTrdiUcQUjD3UuEH-Cu4wm1BMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"A_Tight_Lower_Bound_for_Determinization_of_Transition_Labeled_Büchi_Automata","translated_slug":"","page_count":59,"language":"en","content_type":"Work","summary":null,"owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164273,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164273/thumbnails/1.jpg","file_name":"A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207.pdf","download_url":"https://www.academia.edu/attachments/41164273/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNiw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"A_Tight_Lower_Bound_for_Determinization.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164273/A_Tight_Lower_Bound_for_Determinization_20160114-19510-1wo1207-libre.pdf?1452836895=\u0026response-content-disposition=attachment%3B+filename%3DA_Tight_Lower_Bound_for_Determinization.pdf\u0026Expires=1734524206\u0026Signature=gV5k1bnSCGdNlETBZvDYMeAb99d4nFUmDrFzIlaYlfjXAdkrriwif-1Dsg8gA4cQSedndMBiRcs5VBjGqRV8DvUmfW3OkJbYV0FXXLpEqUxQntWKNkbqOWwiNbEK3Pkg-BibrwdtpKQTJ5A0FJv0qo5E40MIZ24GST81AjeiHa4iMAKkb8Uvfby2yrgEIft8FcVwJE4fJvNgR08RjFM0srne~W6FhRiK2sF2vpyjw5VHmcU9KmeVXQVFt0ZKC~t6KXbu~tRys~raeXbI8R7Lr6afOHLFUxvGEzsiaAAr1jjUkCnmJ1At2eaOY79YpTrdiUcQUjD3UuEH-Cu4wm1BMQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":571143,"name":"Lower Bound","url":"https://www.academia.edu/Documents/in/Lower_Bound"},{"id":575846,"name":"Upper Bound","url":"https://www.academia.edu/Documents/in/Upper_Bound"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105214"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105214/FM_Representability_and_Beyond"><img alt="Research paper thumbnail of FM-Representability and Beyond" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105214/FM_Representability_and_Beyond">FM-Representability and Beyond</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\Sigma_{\rm 2}^{\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\Sigma_{\rm 2}^{\rm 0}–complete and that the set of formulae FM–representing some relations is P03\Pi^{0}_{3}–complete.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105214"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105214"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105214; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105214]").text(description); $(".js-view-count[data-work-id=20105214]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105214; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105214']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105214, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20105214]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105214,"title":"FM-Representability and Beyond","translated_title":"","metadata":{"abstract":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","internal_url":"https://www.academia.edu/20105214/FM_Representability_and_Beyond","translated_internal_url":"","created_at":"2016-01-08T08:13:59.927-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710310,"work_id":20105214,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"FM-Representability and Beyond"}],"downloadable_attachments":[],"slug":"FM_Representability_and_Beyond","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT This work concerns representability of arithmetical notions in finite models. It follows the paper by Marcin Mostowski [1], where the notion of FM–representability has been defined. We discuss how far this notion captures the methodological idea of representing infinite sets in finite but potentially infinite domains. We consider mainly some weakenings of the notion of FM–representability. We prove that relations weakly FM–representable are exactly those being S20\\Sigma_{\\rm 2}^{\\rm 0}–definable. Another weakening of the notion, namely statistical representability, turns out to be equivalent to the original one. Additionally, we consider the complexity of sets of formulae naturally defined in finite models. We state that the set of sentences true in almost all finite arithmetical models is S20\\Sigma_{\\rm 2}^{\\rm 0}–complete and that the set of formulae FM–representing some relations is P03\\Pi^{0}_{3}–complete.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105213"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105213/Coprimality_in_Finite_Models"><img alt="Research paper thumbnail of Coprimality in Finite Models" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105213/Coprimality_in_Finite_Models">Coprimality in Finite Models</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Lecture Notes in Computer Science</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We investigate properties of the coprimality relation within the family of finite models...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\mathrm{FM}((\omega,\bot)). Within FM((w,^))\mathrm{FM}((\omega,\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\mathrm{FM}((\omega,\bot)) is Π01^{\rm 0}_{\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\omega,\bot,\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\omega,\bot,\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\omega,\bot,\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105213"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105213"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105213; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105213]").text(description); $(".js-view-count[data-work-id=20105213]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105213; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105213']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105213, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=20105213]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105213,"title":"Coprimality in Finite Models","translated_title":"","metadata":{"abstract":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"Lecture Notes in Computer Science"},"translated_abstract":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","internal_url":"https://www.academia.edu/20105213/Coprimality_in_Finite_Models","translated_internal_url":"","created_at":"2016-01-08T08:13:59.810-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710308,"work_id":20105213,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Coprimality in Finite Models"}],"downloadable_attachments":[],"slug":"Coprimality_in_Finite_Models","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"ABSTRACT We investigate properties of the coprimality relation within the family of finite models being initial segments of the standard model for coprimality, denoted by FM((w,^))\\mathrm{FM}((\\omega,\\bot)). Within FM((w,^))\\mathrm{FM}((\\omega,\\bot)) we construct an interpretation of addition and multiplication on indices of prime numbers. Consequently, the first order theory of FM((w,^))\\mathrm{FM}((\\omega,\\bot)) is Π01^{\\rm 0}_{\\rm 1}–complete (in contrast to the decidability of the theory of multiplication in the standard model). This result strengthens an analogous theorem of Marcin Mostowski and Anna Wasilewska, 2004, for the divisibility relation. As a byproduct we obtain definitions of addition and multiplication on indices of primes in the model (w,^, £ P2)(\\omega,\\bot,\\leq_{P_2}), where P 2 is the set of primes and products of two different primes and ≤ X is the ordering relation restricted to the set X. This can be compared to the decidability of the first order theory of (w,^, £ P)(\\omega,\\bot,\\leq_P), for P being the set of primes (Maurin, 1997) and to the interpretation of addition and multiplication in (w,^, £ P2)(\\omega,\\bot,\\leq_{P^2}), for P 2 being the set of primes and squares of primes, given by Bès and Richard, 1998.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[],"research_interests":[{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"},{"id":181847,"name":"First-Order Logic","url":"https://www.academia.edu/Documents/in/First-Order_Logic"},{"id":1646429,"name":"Prime Number","url":"https://www.academia.edu/Documents/in/Prime_Number"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105212"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models"><img alt="Research paper thumbnail of Theories of arithmetics in finite models" class="work-thumbnail" src="https://attachments.academia-assets.com/41164160/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models">Theories of arithmetics in finite models</a></div><div class="wp-workCard_item"><span>The Journal of Symbolic Logic</span><span>, 2005</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate theories of initial segments of the standard models for arithmetics. It is easy to...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="11721e9f6321bae3ec77fa50b2531eac" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164160,"asset_id":20105212,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105212"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105212"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105212; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105212]").text(description); $(".js-view-count[data-work-id=20105212]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105212; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105212']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105212, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "11721e9f6321bae3ec77fa50b2531eac" } } $('.js-work-strip[data-work-id=20105212]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105212,"title":"Theories of arithmetics in finite models","translated_title":"","metadata":{"grobid_abstract":"We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.","publication_date":{"day":null,"month":null,"year":2005,"errors":{}},"publication_name":"The Journal of Symbolic Logic","grobid_abstract_attachment_id":41164160},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105212/Theories_of_arithmetics_in_finite_models","translated_internal_url":"","created_at":"2016-01-08T08:13:59.694-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710312,"work_id":20105212,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":0,"name":"Michał Krynicki","title":"Theories of arithmetics in finite models"}],"downloadable_attachments":[{"id":41164160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164160/thumbnails/1.jpg","file_name":"Theories_of_arithmetics_in_finite_models20160114-3921-12h02af.pdf","download_url":"https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_arithmetics_in_finite_models.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164160/Theories_of_arithmetics_in_finite_models20160114-3921-12h02af-libre.pdf?1452836903=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_arithmetics_in_finite_models.pdf\u0026Expires=1734524206\u0026Signature=QoSFYkavDqQ6QYMhsqO6VFM3qh-tFd~bcFM0V4NNwXW8-cjBFMjoqv2Ra3KE4ixRa4LxG~hu9H7ZSCezkhxRud3oPhs5a5wJX2zzBPtNP3PK8n1KkDDHTy14HFwxRCKDKoMkHs8hooHaLcKgP9o6tQ4vWQecq4aEvvkb7vj8hC8glM7FEs81~GHzHWW55w~is8laEduYiLK27e~7yPm8I3oyTYPMMi9AQ6oO5Va9XOaELVSMmvmT2AeuvGxb3rFpyGOZw1iY39LIr6RLHEfncH7qigNWJn8gvENbSraetCuimlGzDaR1jszyludBXfONoBRHyAI5AR0rzq-5O0DtXA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theories_of_arithmetics_in_finite_models","translated_slug":"","page_count":30,"language":"en","content_type":"Work","summary":"We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ2-theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ1-theory of multiplication and order is decidable in finite models as well as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation.","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164160/thumbnails/1.jpg","file_name":"Theories_of_arithmetics_in_finite_models20160114-3921-12h02af.pdf","download_url":"https://www.academia.edu/attachments/41164160/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_arithmetics_in_finite_models.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164160/Theories_of_arithmetics_in_finite_models20160114-3921-12h02af-libre.pdf?1452836903=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_arithmetics_in_finite_models.pdf\u0026Expires=1734524207\u0026Signature=LOD9RedfQRPL~DO~-kKpNe5cmPr~hY2pOxV6wLUzi~T04mzOYShQ~FlLWivGs3RsW3Mi86S~NhToq7dYNny7cVVe9qzaU-TKLeFyOQGljUCHqOkMGA4MsUyp0GC3~eqkWL7Xe8Q4WNK6JeFwf1CG4kH8FaQBHZFrs55WcZQzHGlQn-V0x59uoKIg6l-U54yiJFvb~fyPktM7MhlSsFLEBgVSfSBVMWErGHxyDNMifQTI4zKHg~hVfaeicTsdPItsXubaHD1u4Fax-Cyoul6A0EegW3JKZnl-bn9095PpQl7eAEPjzlQvw8eQMCK39p8f3ROfMQPHbfwaIWodbCEIfg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":803,"name":"Philosophy","url":"https://www.academia.edu/Documents/in/Philosophy"},{"id":8367,"name":"Complexity","url":"https://www.academia.edu/Documents/in/Complexity"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"},{"id":131903,"name":"Arithmetic","url":"https://www.academia.edu/Documents/in/Arithmetic"},{"id":179292,"name":"Symbolic Logic","url":"https://www.academia.edu/Documents/in/Symbolic_Logic"},{"id":321836,"name":"Spectrum","url":"https://www.academia.edu/Documents/in/Spectrum"},{"id":1264826,"name":"Exponential Function","url":"https://www.academia.edu/Documents/in/Exponential_Function"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105211"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann"><img alt="Research paper thumbnail of On a question of Andreas Weiermann" class="work-thumbnail" src="https://attachments.academia-assets.com/41164131/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann">On a question of Andreas Weiermann</a></div><div class="wp-workCard_item"><span>MLQ</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7a55e3b847a8e8aec2d57eb2e3d657d6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164131,"asset_id":20105211,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105211"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105211"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105211; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105211]").text(description); $(".js-view-count[data-work-id=20105211]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105211; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105211']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105211, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7a55e3b847a8e8aec2d57eb2e3d657d6" } } $('.js-work-strip[data-work-id=20105211]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105211,"title":"On a question of Andreas Weiermann","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"MLQ"},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105211/On_a_question_of_Andreas_Weiermann","translated_internal_url":"","created_at":"2016-01-08T08:13:59.570-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710315,"work_id":20105211,"tagging_user_id":41138865,"tagged_user_id":null,"co_author_invite_id":2983266,"email":"h***i@impan.gov.pl","display_order":0,"name":"Henryk Kotlarski","title":"On a question of Andreas Weiermann"}],"downloadable_attachments":[{"id":41164131,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164131/thumbnails/1.jpg","file_name":"On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns.pdf","download_url":"https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_a_question_of_Andreas_Weiermann.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164131/On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns-libre.pdf?1452836904=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_question_of_Andreas_Weiermann.pdf\u0026Expires=1734524207\u0026Signature=PanJmzVU4pXVRdCB3TGzHpLxljYfJZT5H3kZpBYnZuhVajjiUeh3KMvVoJywLDzK-VRqtCAAZzHAYkmp4TUhM6g5fIjWpD4RVerMXHjPA05GWykxPVf30abAn23oq9UBmqQW9X~HEHriTJrpxdIBUIoBGIR7zl~CbbUjAs-J8v9Ak5ADVBw-3ikE4VJCZJrRBQynrMuUyulr-69mZl2wDEcl4iO4z7EdbYpeSeuhZ6n3-MdSYd5WtTMpuWh4BBzI7DcLEkpPauffIkwqO~aHWxyupclns-nage0msjUDazbNFIQW29JDu7zkKz6kRMq5jdW18icRmJge5eHZ9pr9gQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_a_question_of_Andreas_Weiermann","translated_slug":"","page_count":15,"language":"en","content_type":"Work","summary":null,"owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164131,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164131/thumbnails/1.jpg","file_name":"On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns.pdf","download_url":"https://www.academia.edu/attachments/41164131/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_a_question_of_Andreas_Weiermann.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164131/On_a_question_of_Andreas_Weiermann20160114-3921-12xyxns-libre.pdf?1452836904=\u0026response-content-disposition=attachment%3B+filename%3DOn_a_question_of_Andreas_Weiermann.pdf\u0026Expires=1734524207\u0026Signature=PanJmzVU4pXVRdCB3TGzHpLxljYfJZT5H3kZpBYnZuhVajjiUeh3KMvVoJywLDzK-VRqtCAAZzHAYkmp4TUhM6g5fIjWpD4RVerMXHjPA05GWykxPVf30abAn23oq9UBmqQW9X~HEHriTJrpxdIBUIoBGIR7zl~CbbUjAs-J8v9Ak5ADVBw-3ikE4VJCZJrRBQynrMuUyulr-69mZl2wDEcl4iO4z7EdbYpeSeuhZ6n3-MdSYd5WtTMpuWh4BBzI7DcLEkpPauffIkwqO~aHWxyupclns-nage0msjUDazbNFIQW29JDu7zkKz6kRMq5jdW18icRmJge5eHZ9pr9gQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":1190945,"name":"MLQ","url":"https://www.academia.edu/Documents/in/MLQ"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20105210"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies"><img alt="Research paper thumbnail of Degrees of logics with Henkin quantifiers in poor vocabularies" class="work-thumbnail" src="https://attachments.academia-assets.com/41164327/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies">Degrees of logics with Henkin quantifiers in poor vocabularies</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/MarcinMostowski">Marcin Mostowski</a></span></div><div class="wp-workCard_item"><span>Archive for Mathematical Logic</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c38b9dc8089991c04920d28d8af73ef3" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41164327,"asset_id":20105210,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20105210"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20105210"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20105210; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20105210]").text(description); $(".js-view-count[data-work-id=20105210]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20105210; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20105210']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20105210, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "c38b9dc8089991c04920d28d8af73ef3" } } $('.js-work-strip[data-work-id=20105210]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20105210,"title":"Degrees of logics with Henkin quantifiers in poor vocabularies","translated_title":"","metadata":{"grobid_abstract":"We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).","publication_date":{"day":null,"month":null,"year":2004,"errors":{}},"publication_name":"Archive for Mathematical Logic","grobid_abstract_attachment_id":41164327},"translated_abstract":null,"internal_url":"https://www.academia.edu/20105210/Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies","translated_internal_url":"","created_at":"2016-01-08T08:13:59.444-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41138865,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12710309,"work_id":20105210,"tagging_user_id":41138865,"tagged_user_id":41271059,"co_author_invite_id":2371478,"email":"m***i@uw.edu.pl","display_order":0,"name":"Marcin Mostowski","title":"Degrees of logics with Henkin quantifiers in poor vocabularies"}],"downloadable_attachments":[{"id":41164327,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164327/thumbnails/1.jpg","file_name":"Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn.pdf","download_url":"https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Degrees_of_logics_with_Henkin_quantifier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164327/Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn-libre.pdf?1452836971=\u0026response-content-disposition=attachment%3B+filename%3DDegrees_of_logics_with_Henkin_quantifier.pdf\u0026Expires=1734524207\u0026Signature=O7WbfADYBG~3HEXrAdtIn-2ouKl1Y2gB6TlQU~iU5cPxw0sADlZIXKvLA0E0afrfpz0yzCKFDFdCi0KDsqtbHLSLW8lTTPGMOOe9dAPRipDbwk-6DWnKSu8kgle636bBwHOeDCs5rktMl9whRGrvUa7v6iI73kskW0TwkK8VaTmAfflcdOMJkz4Yy6PsUGb0sdnz3KOcfxVDfayrsgEL1izbE7qs9jXn0W6Fco-X9sGAX-HuGhjYzfkosdsGLXK-8pdgW46mW0~ZPb-hMDA6sgfSAVRYCCMZZ1OTS0SxQ9iEtd2e-RyzK~pC0RIT4sWL5kDR51sUyvYNjaS-8EZclw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Degrees_of_logics_with_Henkin_quantifiers_in_poor_vocabularies","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L-tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L * ∅ is of degree 0 . We show that the same holds also for some weaker logics like L ∅ (H ω ) and L ∅ (E ω ).","owner":{"id":41138865,"first_name":"Konrad","middle_initials":null,"last_name":"Zdanowski","page_name":"KonradZdanowski","domain_name":"independent","created_at":"2016-01-08T08:11:22.800-08:00","display_name":"Konrad Zdanowski","url":"https://independent.academia.edu/KonradZdanowski"},"attachments":[{"id":41164327,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41164327/thumbnails/1.jpg","file_name":"Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn.pdf","download_url":"https://www.academia.edu/attachments/41164327/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Degrees_of_logics_with_Henkin_quantifier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41164327/Degrees_of_logics_with_Henkin_quantifier20160114-30991-aotebn-libre.pdf?1452836971=\u0026response-content-disposition=attachment%3B+filename%3DDegrees_of_logics_with_Henkin_quantifier.pdf\u0026Expires=1734524207\u0026Signature=O7WbfADYBG~3HEXrAdtIn-2ouKl1Y2gB6TlQU~iU5cPxw0sADlZIXKvLA0E0afrfpz0yzCKFDFdCi0KDsqtbHLSLW8lTTPGMOOe9dAPRipDbwk-6DWnKSu8kgle636bBwHOeDCs5rktMl9whRGrvUa7v6iI73kskW0TwkK8VaTmAfflcdOMJkz4Yy6PsUGb0sdnz3KOcfxVDfayrsgEL1izbE7qs9jXn0W6Fco-X9sGAX-HuGhjYzfkosdsGLXK-8pdgW46mW0~ZPb-hMDA6sgfSAVRYCCMZZ1OTS0SxQ9iEtd2e-RyzK~pC0RIT4sWL5kDR51sUyvYNjaS-8EZclw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":363,"name":"Set Theory","url":"https://www.academia.edu/Documents/in/Set_Theory"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="19973951"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions"><img alt="Research paper thumbnail of Theories of initial segments of standard models of arithmetics and their complete extensions" class="work-thumbnail" src="https://attachments.academia-assets.com/41270357/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions">Theories of initial segments of standard models of arithmetics and their complete extensions</a></div><div class="wp-workCard_item wp-workCard--coauthors"><span>by </span><span><a class="" data-click-track="profile-work-strip-authors" href="https://u-clermont1.academia.edu/JerzyTomasik">Jerzy Tomasik</a> and <a class="" data-click-track="profile-work-strip-authors" href="https://independent.academia.edu/KonradZdanowski">Konrad Zdanowski</a></span></div><div class="wp-workCard_item"><span>Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate families of finite initial segments of standard models for various arithmetics. We...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="55bdb4850fa5d742fb52c184c457792b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41270357,"asset_id":19973951,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="19973951"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="19973951"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 19973951; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=19973951]").text(description); $(".js-view-count[data-work-id=19973951]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 19973951; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='19973951']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 19973951, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "55bdb4850fa5d742fb52c184c457792b" } } $('.js-work-strip[data-work-id=19973951]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":19973951,"title":"Theories of initial segments of standard models of arithmetics and their complete extensions","translated_title":"","metadata":{"grobid_abstract":"We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.","publication_date":{"day":null,"month":null,"year":2011,"errors":{}},"publication_name":"Theoretical Computer Science","grobid_abstract_attachment_id":41270357},"translated_abstract":null,"internal_url":"https://www.academia.edu/19973951/Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions","translated_internal_url":"","created_at":"2016-01-02T23:18:38.608-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":40854177,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12457138,"work_id":19973951,"tagging_user_id":40854177,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":0,"name":"Michał Krynicki","title":"Theories of initial segments of standard models of arithmetics and their complete extensions"},{"id":12457140,"work_id":19973951,"tagging_user_id":40854177,"tagged_user_id":41138865,"co_author_invite_id":2924721,"email":"k***i@gmail.com","display_order":4194304,"name":"Konrad Zdanowski","title":"Theories of initial segments of standard models of arithmetics and their complete extensions"}],"downloadable_attachments":[{"id":41270357,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41270357/thumbnails/1.jpg","file_name":"Theories_of_initial_segments_of_standard20160116-28334-wmdyzb.pdf","download_url":"https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_initial_segments_of_standard.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41270357/Theories_of_initial_segments_of_standard20160116-28334-wmdyzb-libre.pdf?1452961467=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_initial_segments_of_standard.pdf\u0026Expires=1734524207\u0026Signature=Qv4dVnLRTtsmj2PkGbD6mBekAyoloxyojX0AEnIJIJ8NindsC6g7eRpmpHyK6UDWl8LzwB8M~Xvm9I~E6QpZD5BxDw3YKw8~12QNUqUmKhweYfew4nUFJU2UXm1177VoMKt8EeyM9mnAHsTeeKkroRtsU3j~zTawzcwK~cuYf8GfnpgNsJYGObAJfScH981~Oxtewhmzw5WEcyhIyz-reSHZlHz23vBUjoXrWUI-FhHGqD~X~hpyfgjt-k~sbYLzANZMQXSaWNi7ejSFeTK9-gMNRf0PhcrU-PFfnjZYW9F~5CjQkoSGfVMQvLhruHhOUrsejh1hGcpB3LQjWuONQw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Theories_of_initial_segments_of_standard_models_of_arithmetics_and_their_complete_extensions","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"We investigate families of finite initial segments of standard models for various arithmetics. We give an axiomatization of the theory of sentences true in almost all finite models with addition. We also characterize its complete extensions and relate its infinite models to models of Presburger arithmetic.","owner":{"id":40854177,"first_name":"Jerzy","middle_initials":null,"last_name":"Tomasik","page_name":"JerzyTomasik","domain_name":"u-clermont1","created_at":"2016-01-02T23:17:53.746-08:00","display_name":"Jerzy Tomasik","url":"https://u-clermont1.academia.edu/JerzyTomasik"},"attachments":[{"id":41270357,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41270357/thumbnails/1.jpg","file_name":"Theories_of_initial_segments_of_standard20160116-28334-wmdyzb.pdf","download_url":"https://www.academia.edu/attachments/41270357/download_file?st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&st=MTczNDUyMDYwNyw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theories_of_initial_segments_of_standard.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41270357/Theories_of_initial_segments_of_standard20160116-28334-wmdyzb-libre.pdf?1452961467=\u0026response-content-disposition=attachment%3B+filename%3DTheories_of_initial_segments_of_standard.pdf\u0026Expires=1734524207\u0026Signature=Qv4dVnLRTtsmj2PkGbD6mBekAyoloxyojX0AEnIJIJ8NindsC6g7eRpmpHyK6UDWl8LzwB8M~Xvm9I~E6QpZD5BxDw3YKw8~12QNUqUmKhweYfew4nUFJU2UXm1177VoMKt8EeyM9mnAHsTeeKkroRtsU3j~zTawzcwK~cuYf8GfnpgNsJYGObAJfScH981~Oxtewhmzw5WEcyhIyz-reSHZlHz23vBUjoXrWUI-FhHGqD~X~hpyfgjt-k~sbYLzANZMQXSaWNi7ejSFeTK9-gMNRf0PhcrU-PFfnjZYW9F~5CjQkoSGfVMQvLhruHhOUrsejh1hGcpB3LQjWuONQw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":17100,"name":"Theoretical Computer Science","url":"https://www.academia.edu/Documents/in/Theoretical_Computer_Science"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/google_contacts-0dfb882d836b94dbcb4a2d123d6933fc9533eda5be911641f20b4eb428429600.js"], function() { // from javascript_helper.rb $('.js-google-connect-button').click(function(e) { e.preventDefault(); GoogleContacts.authorize_and_show_contacts(); Aedu.Dismissibles.recordClickthrough("WowProfileImportContactsPrompt"); }); $('.js-update-biography-button').click(function(e) { e.preventDefault(); Aedu.Dismissibles.recordClickthrough("UpdateUserBiographyPrompt"); $.ajax({ url: $r.api_v0_profiles_update_about_path({ subdomain_param: 'api', about: "", }), type: 'PUT', success: function(response) { location.reload(); } }); }); $('.js-work-creator-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_document_path({ source: encodeURIComponent(""), }); }); $('.js-video-upload-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_video_path({ source: encodeURIComponent(""), }); }); $('.js-do-this-later-button').click(function() { $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("WowProfileImportContactsPrompt"); }); $('.js-update-biography-do-this-later-button').click(function(){ $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("UpdateUserBiographyPrompt"); }); $('.wow-profile-mentions-upsell--close').click(function(){ $('.wow-profile-mentions-upsell--panel').hide(); Aedu.Dismissibles.recordDismissal("WowProfileMentionsUpsell"); }); $('.wow-profile-mentions-upsell--button').click(function(){ Aedu.Dismissibles.recordClickthrough("WowProfileMentionsUpsell"); }); new WowProfile.SocialRedesignUserWorks({ initialWorksOffset: 20, allWorksOffset: 20, maxSections: 1 }) }); </script> </div></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile_edit-5ea339ee107c863779f560dd7275595239fed73f1a13d279d2b599a28c0ecd33.js","https://a.academia-assets.com/assets/add_coauthor-22174b608f9cb871d03443cafa7feac496fb50d7df2d66a53f5ee3c04ba67f53.js","https://a.academia-assets.com/assets/tab-dcac0130902f0cc2d8cb403714dd47454f11fc6fb0e99ae6a0827b06613abc20.js","https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js"], function() { // from javascript_helper.rb window.ae = window.ae || {}; window.ae.WowProfile = window.ae.WowProfile || {}; if(Aedu.User.current && Aedu.User.current.id === $viewedUser.id) { window.ae.WowProfile.current_user_edit = {}; new WowProfileEdit.EditUploadView({ el: '.js-edit-upload-button-wrapper', model: window.$current_user, }); new AddCoauthor.AddCoauthorsController(); } var userInfoView = new WowProfile.SocialRedesignUserInfo({ recaptcha_key: "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB" }); WowProfile.router = new WowProfile.Router({ userInfoView: userInfoView }); Backbone.history.start({ pushState: true, root: "/" + $viewedUser.page_name }); new WowProfile.UserWorksNav() }); </script> </div> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span   ="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "4a7cbd1e7e3fe952bb3d055b0d30534d5a287d811283d38f6cb2819cc107e24a", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="hp3pgGXKIgW7mlq6AEeD5IcNyNA/O2pV0svsyAoOyvEGNhJZffu/bqFGAaFjM/XNE1I6wT3jkKws8sfukhicSQ==" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://independent.academia.edu/KonradZdanowski" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input name="utf8" type="hidden" value="✓" autocomplete="off" /><input type="hidden" name="authenticity_token" value="FSkgvHlbQdtFNKGzuKJ1oxix1z/bGMQ1fguLSijOurCVgttlYWrcsF/o+qjb1gOKjO4lLtnAPsyAMqBssNjsCA==" autocomplete="off" /><p>Enter the email address you signed up with and we'll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><script src="https://recaptcha.net/recaptcha/api.js" async defer></script> <script> var invisibleRecaptchaSubmit = function () { var closestForm = function (ele) { var curEle = ele.parentNode; while (curEle.nodeName !== 'FORM' && curEle.nodeName !== 'BODY'){ curEle = curEle.parentNode; } return curEle.nodeName === 'FORM' ? curEle : null }; var eles = document.getElementsByClassName('g-recaptcha'); if (eles.length > 0) { var form = closestForm(eles[0]); if (form) { form.submit(); } } }; </script> <input type="submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" data-callback="invisibleRecaptchaSubmit" class="g-recaptcha btn btn-primary btn-block" value="Email me a link" value=""/> </form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account? <a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div class="bootstrap" id="footer"><div class="footer-content clearfix text-center padding-top-7x" style="width:100%;"><ul class="footer-links-secondary footer-links-wide list-inline margin-bottom-1x"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/journals">Academia.edu Journals</a></li><li><a rel="nofollow" href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg> <strong>We're Hiring!</strong></a></li><li><a rel="nofollow" href="https://support.academia.edu/"><svg style="width: 12px; height: 12px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg> <strong>Help Center</strong></a></li></ul><ul class="footer-links-tertiary list-inline margin-bottom-1x"><li class="small">Find new research papers in:</li><li class="small"><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul></div></div><div class="DesignSystem" id="credit" style="width:100%;"><ul class="u-pl0x footer-links-legal list-inline"><li><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia ©2024</li></ul></div><script> //<![CDATA[ window.detect_gmtoffset = true; window.Academia && window.Academia.set_gmtoffset && Academia.set_gmtoffset('/gmtoffset'); //]]> </script> <div id='overlay_background'></div> <div id='bootstrap-modal-container' class='bootstrap'></div> <div id='ds-modal-container' class='bootstrap DesignSystem'></div> <div id='full-screen-modal'></div> </div> </body> </html>