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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 Marcin Mostowski</h3></div><div class="js-work-strip profile--work_container" data-work-id="20160343"><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/20160343/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C"><img alt="Research paper thumbnail of Recursive complexity of the Carnap first order modal logic C" class="work-thumbnail" src="https://attachments.academia-assets.com/41233044/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/20160343/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C">Recursive complexity of the Carnap first order modal logic C</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider first order modal logic C firstly defined by Carnap in Meaning and Necessity [1]. 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 consider first order modal logic C firstly defined by Carnap in Meaning and Necessity [1]. We prove elimination of nested modalities for this logic, which gives additionally Skolem-Löwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0 ′ . We compare this logic with the logics of Henkin quantifiers, Σ 1 1 logic, and SO. We also shortly discuss properties of the logic C in finite models.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1885f94b926779071e02a99c9a63a17b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41233044,"asset_id":20160343,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41233044/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160343"><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="20160343"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160343; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160343]").text(description); $(".js-view-count[data-work-id=20160343]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160343; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160343']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160343, 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: "1885f94b926779071e02a99c9a63a17b" } } $('.js-work-strip[data-work-id=20160343]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160343,"title":"Recursive complexity of the Carnap first order modal logic C","translated_title":"","metadata":{"ai_title_tag":"Recursion and Complexity in Carnap's Modal Logic C","grobid_abstract":"We consider first order modal logic C firstly defined by Carnap in Meaning and Necessity [1]. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20160342"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20160342/O_problemie_termin%C3%B3w_pustych"><img alt="Research paper thumbnail of O problemie terminów pustych" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20160342/O_problemie_termin%C3%B3w_pustych">O problemie terminów pustych</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20160342"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20160342"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160342; 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$(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="20160341"><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/20160341/Quantifiers_some_problems_and_ideas"><img alt="Research paper thumbnail of Quantifiers, some problems and ideas" 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/20160341/Quantifiers_some_problems_and_ideas">Quantifiers, some problems and ideas</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This is a general discussion on quantifiers. Starting from the general definitions of Mo...</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 is a general discussion on quantifiers. Starting from the general definitions of Mostowski and Lindström, the authors present various generalizations, as currently considered in abstract model theory. In the final part, the authors briefly discuss the role of quantifiers in logic (notably, in finite model theory), computer science and linguistics.</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="20160341"><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="20160341"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160341; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160341]").text(description); $(".js-view-count[data-work-id=20160341]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160341; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160341']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160341, 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" } } $('.js-work-strip[data-work-id=20160341]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160341,"title":"Quantifiers, some problems and ideas","translated_title":"","metadata":{"abstract":"ABSTRACT This is a general discussion on quantifiers. 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$(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. 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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="2094651"><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/2094651/Semantic_bounds_for_everyday_language"><img alt="Research paper thumbnail of Semantic bounds for everyday language" class="work-thumbnail" src="https://attachments.academia-assets.com/31307126/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/2094651/Semantic_bounds_for_everyday_language">Semantic bounds for everyday language</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://uva.academia.edu/JakubSzymanik">Jakub Szymanik</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 class="js-work-more-abstract-truncated">We consider the notion of everyday language. We claim that everyday language is semantically boun...</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 consider the notion of everyday language. We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic. Two arguments for this thesis are formulated. First, we show that Barwise's so-called test of negation normality works properly only when assuming our main thesis. Second, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. We show that in both cases they are bounded by second-order existential properties. Moreover, there are known examples of everyday language sentences that are the most difficult in this class ( NPTIME-complete). Brought to you by | Bibliotheek der Rijksuniversiteit (Bibliotheek der Rijksuniversite Authenticated | 172.16.1.226 Download Date | 2/17/12 5:02 PM</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6ad56b6450bb5a8ed60e0d9d178f11d4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":31307126,"asset_id":2094651,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/31307126/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="2094651"><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="2094651"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 2094651; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=2094651]").text(description); $(".js-view-count[data-work-id=2094651]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 2094651; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='2094651']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 2094651, 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: "6ad56b6450bb5a8ed60e0d9d178f11d4" } } $('.js-work-strip[data-work-id=2094651]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":2094651,"title":"Semantic bounds for everyday language","translated_title":"","metadata":{"publisher":"degruyter.com","ai_title_tag":"Bounded Semantics of Everyday Language in Second-Order Logic","grobid_abstract":"We consider the notion of everyday language. 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We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic. Two arguments for this thesis are formulated. First, we show that Barwise's so-called test of negation normality works properly only when assuming our main thesis. Second, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. We show that in both cases they are bounded by second-order existential properties. Moreover, there are known examples of everyday language sentences that are the most difficult in this class ( NPTIME-complete). 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$(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="20160335"><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/20160335/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C"><img alt="Research paper thumbnail of Recursive complexity of the Carnap first order modal logic C" class="work-thumbnail" src="https://attachments.academia-assets.com/41049509/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/20160335/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C">Recursive complexity of the Carnap first order modal logic C</a></div><div class="wp-workCard_item"><span>MLQ</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Key words Modal logic, Carnap modal logic, alethic modalities, degrees of unsolvability, finite m...</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">Key words Modal logic, Carnap modal logic, alethic modalities, degrees of unsolvability, finite models, second order logic, Henkin quantifiers.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="825f184ccbb820688a4d91fe1c137e89" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41049509,"asset_id":20160335,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41049509/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160335"><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="20160335"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160335; 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$(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="20160334"><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/20160334/Arithmetic_of_divisibility_in_finite_models"><img alt="Research paper thumbnail of Arithmetic of divisibility in finite models" class="work-thumbnail" src="https://attachments.academia-assets.com/41984276/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/20160334/Arithmetic_of_divisibility_in_finite_models">Arithmetic of divisibility 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/AnnaW140">Anna W.</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>MLQ</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove that the finite-model version of arithmetic with the divisibility relation is undecidabl...</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 prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f489367a8d0f764103285cecd7f4356" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41984276,"asset_id":20160334,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41984276/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160334"><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="20160334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160334]").text(description); $(".js-view-count[data-work-id=20160334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160334']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160334, 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: "1f489367a8d0f764103285cecd7f4356" } } $('.js-work-strip[data-work-id=20160334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160334,"title":"Arithmetic of divisibility in finite models","translated_title":"","metadata":{"grobid_abstract":"We prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). 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Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.","owner":{"id":41271059,"first_name":"Marcin","middle_initials":null,"last_name":"Mostowski","page_name":"MarcinMostowski","domain_name":"independent","created_at":"2016-01-11T04:08:53.072-08:00","display_name":"Marcin Mostowski","url":"https://independent.academia.edu/MarcinMostowski"},"attachments":[{"id":41984276,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41984276/thumbnails/1.jpg","file_name":"malq.200310086.pdf20160203-19516-eli87c","download_url":"https://www.academia.edu/attachments/41984276/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Arithmetic_of_divisibility_in_finite_mod.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41984276/malq.200310086-libre.pdf20160203-19516-eli87c?1454538516=\u0026response-content-disposition=attachment%3B+filename%3DArithmetic_of_divisibility_in_finite_mod.pdf\u0026Expires=1734534279\u0026Signature=EpyOphIu7HCoCdqyUJiGAYofDSpDjaqgrAyPKMXyRSSxaqmK9duqQL4HMO79~h8jnk~976pnzQ-b49bQ271TifnRn90iF-Z0B~w6SXuMA11jxBAra-V4D9fqC14~w~Blg8rfMbsaaPQgK-b20aXQ2EjkG8ffgjmWvQF38~aZZPoRYiGFc0ysC6YlyqnnPI27iO34aiR8206T46~AS2LK~S4TheBgYm~p8SU7JpO2HAAQE-72Yaiw7beLPAQb-cga-d400GgZmxxfWnewqQ8rLbWJA3IoVKCvrYDZgjNGtpeQt19UTnukSlvSoVDQ0~okV~19wArspyezfaRY3ocF3Q__\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=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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 . 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Mostowski, Decidability problems in languages with Henkin quantifiers</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0b6a537ddf28081a5a984e63417306c5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41240346,"asset_id":20160333,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41240346/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160333"><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="20160333"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160333; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160333]").text(description); $(".js-view-count[data-work-id=20160333]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160333; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160333']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160333, 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: "0b6a537ddf28081a5a984e63417306c5" } } $('.js-work-strip[data-work-id=20160333]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160333,"title":"Decidability problems in languages with Henkin quantifiers","translated_title":"","metadata":{"grobid_abstract":"Krynicki, M. and M. 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We show that if Hintikka is right then recognizing the truth value of the sentence in nite models is an NP-complete problem. We discuss also possible conclusions from this observation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="22ed2b873fd2869c283c68a4dfb7f204" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41240173,"asset_id":20160332,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41240173/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160332"><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="20160332"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160332; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160332]").text(description); $(".js-view-count[data-work-id=20160332]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160332; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160332']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160332, 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: "22ed2b873fd2869c283c68a4dfb7f204" } } $('.js-work-strip[data-work-id=20160332]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160332,"title":"Computational complexity of the semantics of some natural language constructions","translated_title":"","metadata":{"grobid_abstract":"We consider an example of a sentence which according to Hintikka's claim essentially requires for its logical form a Henkin quantier. 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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=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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. 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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 consider first order modal logic C firstly defined by Carnap in Meaning and Necessity [1]. We prove elimination of nested modalities for this logic, which gives additionally Skolem-Löwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0 ′ . We compare this logic with the logics of Henkin quantifiers, Σ 1 1 logic, and SO. We also shortly discuss properties of the logic C in finite models.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1885f94b926779071e02a99c9a63a17b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41233044,"asset_id":20160343,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41233044/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160343"><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="20160343"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160343; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160343]").text(description); $(".js-view-count[data-work-id=20160343]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160343; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160343']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160343, 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: "1885f94b926779071e02a99c9a63a17b" } } $('.js-work-strip[data-work-id=20160343]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160343,"title":"Recursive complexity of the Carnap first order modal logic C","translated_title":"","metadata":{"ai_title_tag":"Recursion and Complexity in Carnap's Modal Logic C","grobid_abstract":"We consider first order modal logic C firstly defined by Carnap in Meaning and Necessity [1]. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="20160336"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/20160336/Henkin_Quantifiers"><img alt="Research paper thumbnail of Henkin Quantifiers" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/20160336/Henkin_Quantifiers">Henkin Quantifiers</a></div><div class="wp-workCard_item"><span>Quantifiers: Logics, Models and Computation</span><span>, 1995</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="20160336"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="20160336"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160336; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160336]").text(description); $(".js-view-count[data-work-id=20160336]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160336; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160336']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160336, 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" } } $('.js-work-strip[data-work-id=20160336]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160336,"title":"Henkin Quantifiers","translated_title":"","metadata":{"publication_date":{"day":null,"month":null,"year":1995,"errors":{}},"publication_name":"Quantifiers: Logics, Models and Computation"},"translated_abstract":null,"internal_url":"https://www.academia.edu/20160336/Henkin_Quantifiers","translated_internal_url":"","created_at":"2016-01-11T04:10:20.577-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41271059,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12813187,"work_id":20160336,"tagging_user_id":41271059,"tagged_user_id":null,"co_author_invite_id":2924720,"email":"m***i@uksw.edu.pl","display_order":0,"name":"Michał Krynicki","title":"Henkin Quantifiers"}],"downloadable_attachments":[],"slug":"Henkin_Quantifiers","translated_slug":"","page_count":null,"language":"fi","content_type":"Work","summary":null,"owner":{"id":41271059,"first_name":"Marcin","middle_initials":null,"last_name":"Mostowski","page_name":"MarcinMostowski","domain_name":"independent","created_at":"2016-01-11T04:08:53.072-08:00","display_name":"Marcin Mostowski","url":"https://independent.academia.edu/MarcinMostowski"},"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="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="2094651"><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/2094651/Semantic_bounds_for_everyday_language"><img alt="Research paper thumbnail of Semantic bounds for everyday language" class="work-thumbnail" src="https://attachments.academia-assets.com/31307126/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/2094651/Semantic_bounds_for_everyday_language">Semantic bounds for everyday language</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://uva.academia.edu/JakubSzymanik">Jakub Szymanik</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 class="js-work-more-abstract-truncated">We consider the notion of everyday language. We claim that everyday language is semantically boun...</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 consider the notion of everyday language. We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic. Two arguments for this thesis are formulated. First, we show that Barwise's so-called test of negation normality works properly only when assuming our main thesis. Second, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. We show that in both cases they are bounded by second-order existential properties. Moreover, there are known examples of everyday language sentences that are the most difficult in this class ( NPTIME-complete). Brought to you by | Bibliotheek der Rijksuniversiteit (Bibliotheek der Rijksuniversite Authenticated | 172.16.1.226 Download Date | 2/17/12 5:02 PM</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6ad56b6450bb5a8ed60e0d9d178f11d4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":31307126,"asset_id":2094651,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/31307126/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="2094651"><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="2094651"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 2094651; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=2094651]").text(description); $(".js-view-count[data-work-id=2094651]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 2094651; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='2094651']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 2094651, 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: "6ad56b6450bb5a8ed60e0d9d178f11d4" } } $('.js-work-strip[data-work-id=2094651]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":2094651,"title":"Semantic bounds for everyday language","translated_title":"","metadata":{"publisher":"degruyter.com","ai_title_tag":"Bounded Semantics of Everyday Language in Second-Order Logic","grobid_abstract":"We consider the notion of everyday language. We claim that everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic. Two arguments for this thesis are formulated. First, we show that Barwise's so-called test of negation normality works properly only when assuming our main thesis. Second, we discuss the argument from practical computability for finite universes. Everyday language sentences are directly or indirectly verifiable. We show that in both cases they are bounded by second-order existential properties. Moreover, there are known examples of everyday language sentences that are the most difficult in this class ( NPTIME-complete). 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$(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="20160335"><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/20160335/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C"><img alt="Research paper thumbnail of Recursive complexity of the Carnap first order modal logic C" class="work-thumbnail" src="https://attachments.academia-assets.com/41049509/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/20160335/Recursive_complexity_of_the_Carnap_first_order_modal_logic_C">Recursive complexity of the Carnap first order modal logic C</a></div><div class="wp-workCard_item"><span>MLQ</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Key words Modal logic, Carnap modal logic, alethic modalities, degrees of unsolvability, finite m...</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">Key words Modal logic, Carnap modal logic, alethic modalities, degrees of unsolvability, finite models, second order logic, Henkin quantifiers.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="825f184ccbb820688a4d91fe1c137e89" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41049509,"asset_id":20160335,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41049509/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160335"><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="20160335"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160335; 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$(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="20160334"><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/20160334/Arithmetic_of_divisibility_in_finite_models"><img alt="Research paper thumbnail of Arithmetic of divisibility in finite models" class="work-thumbnail" src="https://attachments.academia-assets.com/41984276/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/20160334/Arithmetic_of_divisibility_in_finite_models">Arithmetic of divisibility 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/AnnaW140">Anna W.</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>MLQ</span><span>, 2004</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove that the finite-model version of arithmetic with the divisibility relation is undecidabl...</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 prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1f489367a8d0f764103285cecd7f4356" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41984276,"asset_id":20160334,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41984276/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160334"><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="20160334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160334]").text(description); $(".js-view-count[data-work-id=20160334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160334']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160334, 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: "1f489367a8d0f764103285cecd7f4356" } } $('.js-work-strip[data-work-id=20160334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160334,"title":"Arithmetic of divisibility in finite models","translated_title":"","metadata":{"grobid_abstract":"We prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.","publication_date":{"day":null,"month":null,"year":2004,"errors":{}},"publication_name":"MLQ","grobid_abstract_attachment_id":41984276},"translated_abstract":null,"internal_url":"https://www.academia.edu/20160334/Arithmetic_of_divisibility_in_finite_models","translated_internal_url":"","created_at":"2016-01-11T04:10:19.846-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":41271059,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[{"id":12813191,"work_id":20160334,"tagging_user_id":41271059,"tagged_user_id":200061400,"co_author_invite_id":3006449,"email":"a***a@gmail.com","display_order":0,"name":"Anna W.","title":"Arithmetic of divisibility in finite models"}],"downloadable_attachments":[{"id":41984276,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41984276/thumbnails/1.jpg","file_name":"malq.200310086.pdf20160203-19516-eli87c","download_url":"https://www.academia.edu/attachments/41984276/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Arithmetic_of_divisibility_in_finite_mod.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41984276/malq.200310086-libre.pdf20160203-19516-eli87c?1454538516=\u0026response-content-disposition=attachment%3B+filename%3DArithmetic_of_divisibility_in_finite_mod.pdf\u0026Expires=1734534279\u0026Signature=EpyOphIu7HCoCdqyUJiGAYofDSpDjaqgrAyPKMXyRSSxaqmK9duqQL4HMO79~h8jnk~976pnzQ-b49bQ271TifnRn90iF-Z0B~w6SXuMA11jxBAra-V4D9fqC14~w~Blg8rfMbsaaPQgK-b20aXQ2EjkG8ffgjmWvQF38~aZZPoRYiGFc0ysC6YlyqnnPI27iO34aiR8206T46~AS2LK~S4TheBgYm~p8SU7JpO2HAAQE-72Yaiw7beLPAQb-cga-d400GgZmxxfWnewqQ8rLbWJA3IoVKCvrYDZgjNGtpeQt19UTnukSlvSoVDQ0~okV~19wArspyezfaRY3ocF3Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Arithmetic_of_divisibility_in_finite_models","translated_slug":"","page_count":6,"language":"en","content_type":"Work","summary":"We prove that the finite-model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π 0 1 -complete set of theorems). Additionally we prove FM-representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 . We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only.","owner":{"id":41271059,"first_name":"Marcin","middle_initials":null,"last_name":"Mostowski","page_name":"MarcinMostowski","domain_name":"independent","created_at":"2016-01-11T04:08:53.072-08:00","display_name":"Marcin Mostowski","url":"https://independent.academia.edu/MarcinMostowski"},"attachments":[{"id":41984276,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/41984276/thumbnails/1.jpg","file_name":"malq.200310086.pdf20160203-19516-eli87c","download_url":"https://www.academia.edu/attachments/41984276/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Arithmetic_of_divisibility_in_finite_mod.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/41984276/malq.200310086-libre.pdf20160203-19516-eli87c?1454538516=\u0026response-content-disposition=attachment%3B+filename%3DArithmetic_of_divisibility_in_finite_mod.pdf\u0026Expires=1734534279\u0026Signature=EpyOphIu7HCoCdqyUJiGAYofDSpDjaqgrAyPKMXyRSSxaqmK9duqQL4HMO79~h8jnk~976pnzQ-b49bQ271TifnRn90iF-Z0B~w6SXuMA11jxBAra-V4D9fqC14~w~Blg8rfMbsaaPQgK-b20aXQ2EjkG8ffgjmWvQF38~aZZPoRYiGFc0ysC6YlyqnnPI27iO34aiR8206T46~AS2LK~S4TheBgYm~p8SU7JpO2HAAQE-72Yaiw7beLPAQb-cga-d400GgZmxxfWnewqQ8rLbWJA3IoVKCvrYDZgjNGtpeQt19UTnukSlvSoVDQ0~okV~19wArspyezfaRY3ocF3Q__\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=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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. 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Mostowski, Decidability problems in languages with Henkin quantifiers</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0b6a537ddf28081a5a984e63417306c5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41240346,"asset_id":20160333,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41240346/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160333"><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="20160333"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160333; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160333]").text(description); $(".js-view-count[data-work-id=20160333]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160333; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160333']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160333, 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: "0b6a537ddf28081a5a984e63417306c5" } } $('.js-work-strip[data-work-id=20160333]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160333,"title":"Decidability problems in languages with Henkin quantifiers","translated_title":"","metadata":{"grobid_abstract":"Krynicki, M. and M. 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We show that if Hintikka is right then recognizing the truth value of the sentence in nite models is an NP-complete problem. We discuss also possible conclusions from this observation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="22ed2b873fd2869c283c68a4dfb7f204" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":41240173,"asset_id":20160332,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/41240173/download_file?st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&st=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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="20160332"><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="20160332"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20160332; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20160332]").text(description); $(".js-view-count[data-work-id=20160332]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 20160332; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='20160332']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 20160332, 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: "22ed2b873fd2869c283c68a4dfb7f204" } } $('.js-work-strip[data-work-id=20160332]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":20160332,"title":"Computational complexity of the semantics of some natural language constructions","translated_title":"","metadata":{"grobid_abstract":"We consider an example of a sentence which according to Hintikka's claim essentially requires for its logical form a Henkin quantier. 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$(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=MTczNDUzMDY3OSw4LjIyMi4yMDguMTQ2&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. 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