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class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://independent.academia.edu/HariSeldon32">Hari Seldon</a></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a data-nosnippet="" href="https://independent.academia.edu/DSowinski"><img class="profile-avatar u-positionAbsolute" alt="Damian Sowinski related author profile picture" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" src="https://gravatar.com/avatar/0f58d38684a8d1f4b9b6bb6366a516c3?s=200" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://independent.academia.edu/DSowinski">Damian Sowinski</a></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a 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src="https://0.academia-photos.com/18670/6292/30672955/s200_eric.kerr.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://nus.academia.edu/EricTKerr">Eric Kerr</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">National University of Singapore</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a data-nosnippet="" href="https://herts.academia.edu/ChristophSchulz"><img class="profile-avatar u-positionAbsolute" alt="Christoph Schulz related author profile picture" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/1734975/596989/4256680/s200_christoph.schulz.jpg" /></a></div><div class="suggested-user-card__user-info"><a 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class="suggested-user-card__user-info__subheader ds2-5-body-xs">Ben Gurion University of the Negev</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a data-nosnippet="" href="https://mjc.academia.edu/CarsonGrubaugh"><img class="profile-avatar u-positionAbsolute" alt="Carson Grubaugh related author profile picture" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/34742410/10484620/13090606/s200_carson.grubaugh.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://mjc.academia.edu/CarsonGrubaugh">Carson Grubaugh</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Modesto Junior College</p></div></div><div class="suggested-user-card"><div 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class="ri-more-link js-profile-ri-list-card" data-click-track="profile-user-info-primary-research-interest" data-has-card-for-ri-list="631545">View All (10)</a></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="631545" href="https://www.academia.edu/Documents/in/Logic"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://ufrj.academia.edu/FranciscoDoria","location":"/FranciscoDoria","scheme":"https","host":"ufrj.academia.edu","port":null,"pathname":"/FranciscoDoria","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Logic"]}" data-trace="false" data-dom-id="Pill-react-component-b7c4e56c-2211-41f1-b41b-60a7d2b0ab8d"></div> <div 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id="Pill-react-component-60184212-8e48-43b2-a07d-4ed5dbfe4762"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="nav-container backbone-profile-documents-nav hidden-xs"><ul class="nav-tablist" role="tablist"><li class="nav-chip active" role="presentation"><a data-section-name="" data-toggle="tab" href="#all" role="tab">all</a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Books" data-toggle="tab" href="#books" role="tab" title="Books"><span>1</span> <span class="ds2-5-body-sm-bold">Books</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Papers" data-toggle="tab" href="#papers" role="tab" title="Papers"><span>77</span> <span class="ds2-5-body-sm-bold">Papers</span></a></li><li class="nav-chip" role="presentation"><a class="js-profile-docs-nav-section u-textTruncate" data-click-track="profile-works-tab" data-section-name="Drafts" data-toggle="tab" href="#drafts" role="tab" title="Drafts"><span>1</span> <span class="ds2-5-body-sm-bold">Drafts</span></a></li></ul></div><div class="divider ds-divider-16" style="margin: 0px;"></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Books" id="Books"><h3 class="profile--tab_heading_container">Books by Francisco Antonio Doria</h3></div><div class="js-work-strip profile--work_container" data-work-id="1028034"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/1028034/Goedels_Way"><img alt="Research paper thumbnail of Goedel's Way" 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">Goedel's Way</div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">My book with Greg Chaitin and Newton da Costa. Heretic viewpoints. </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="1028034"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="1028034"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 1028034; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=1028034]").text(description); $(".js-view-count[data-work-id=1028034]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 1028034; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='1028034']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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" } } $('.js-work-strip[data-work-id=1028034]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":1028034,"title":"Goedel's Way","translated_title":"","metadata":{"abstract":"My book with Greg Chaitin and Newton da Costa. 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","owner":{"id":631545,"first_name":"Francisco Antonio","middle_initials":"","last_name":"Doria","page_name":"FranciscoDoria","domain_name":"ufrj","created_at":"2011-07-31T14:20:54.461-07:00","display_name":"Francisco Antonio Doria","url":"https://ufrj.academia.edu/FranciscoDoria"},"attachments":[],"research_interests":[],"urls":[{"id":140387,"url":"http://www.taylorandfrancis.com/books/details/9780415690850/"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-1028034-figures'); } }); </script> <div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Francisco Antonio Doria</h3></div><div class="js-work-strip profile--work_container" data-work-id="96762497"><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/96762497/The_Map_and_the_Territory"><img alt="Research paper thumbnail of The Map and the Territory" class="work-thumbnail" src="https://attachments.academia-assets.com/98570856/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/96762497/The_Map_and_the_Territory">The Map and the Territory</a></div><div class="wp-workCard_item"><span>The Frontiers Collection</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Science is a constructed narrative of the natural world based on information gathering and its su...</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">Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. In this essay, we develop a novel approach to the epistemic foundations of the scientific narrative, as based on our experiential interactions with the natural world. We first review some of the basic aspects of both Bayesian statistics and Shannon's information theory as applied to the construction of meaningful conceptualization of the natural world. This conceptualization is rendered through the maps we construct of the world based on our limited knowledge of reality. We propose a path from experience to information and physics based on the notion that information is experience that induces change in an Epistemic Agent (EA): the change may be local and focused to a minor aspect of reality or it may be broad and worldview-changing. We illustrate our approach through an analysis of a measure of spatial complexity proposed by one of us called Configuration Entropy (CE), and establish a link between experience at the cognitive level and information content, showing that the CE is a quantitative measure of how much information in spatial-complexity the external world hides from an EA. All philosophy is based on two things only: curiosity and poor eyesight. The trouble is, we want to know more than we can see. Bernard le Bovier de Fontenelle a To appear in Map and Territory-Exploring the Foundations of Science, Thought and Reality, ed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1c6d514ffb72831b007a64604eb6a43b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570856,"asset_id":96762497,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570856/download_file?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="96762497"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762497"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762497; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762497]").text(description); $(".js-view-count[data-work-id=96762497]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762497; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762497']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "1c6d514ffb72831b007a64604eb6a43b" } } $('.js-work-strip[data-work-id=96762497]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762497,"title":"The Map and the Territory","translated_title":"","metadata":{"publisher":"Springer International Publishing","ai_title_tag":"From Experience to Information: The Epistemic Foundations of Science","grobid_abstract":"Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. 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We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.</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="96762495"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762495"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762495; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762495]").text(description); $(".js-view-count[data-work-id=96762495]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762495; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762495']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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" } } $('.js-work-strip[data-work-id=96762495]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762495,"title":"Gödel Incompleteness and the Empirical Sciences","translated_title":"","metadata":{"abstract":"We show how widespread are metamathematical phenomena in mathematics and in the sciences which rely on mathematics. 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Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b96003029bd2e84d81eb0a3a2761b4b5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570853,"asset_id":96762492,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570853/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96762492"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762492"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762492; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762492]").text(description); $(".js-view-count[data-work-id=96762492]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762492; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762492']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "b96003029bd2e84d81eb0a3a2761b4b5" } } $('.js-work-strip[data-work-id=96762492]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762492,"title":"Consequences of an exotic definition for P NP q","translated_title":"","metadata":{"abstract":"We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. 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We finally derive a consistency result for P NP itself.","internal_url":"https://www.academia.edu/96762492/Consequences_of_an_exotic_definition_for_P_NP_q","translated_internal_url":"","created_at":"2023-02-12T05:58:26.241-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":631545,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":98570853,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/98570853/thumbnails/1.jpg","file_name":"AMC7887page.pdf","download_url":"https://www.academia.edu/attachments/98570853/download_file","bulk_download_file_name":"Consequences_of_an_exotic_definition_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/98570853/AMC7887page-libre.pdf?1676212326=\u0026response-content-disposition=attachment%3B+filename%3DConsequences_of_an_exotic_definition_for.pdf\u0026Expires=1743333191\u0026Signature=f6lPBIanDZLuY-xF66BEk8kb7L4iBVm7EhMSq-~lukVKnsQ9IpmwM0lqtV1gbo37WVlq2ISM7q3a8J-l4cXMT13mi1ej1FNIDZt0av-jE167rWwqgJxhyGSiEpfFVhhh8mEwt~ZHyE~7haqxczez8UdJGxt6hfjbWxoJ1ZfRiQg6piv1zgx~ZRe-nqejigFSh8p2D6KHQpFM~4pyrQnbNiSlkaydXBVTlrJVFgRnCxSlUjJNq4RAAt8i4l70ra7-BJ~C16CWrjVQEU4BKtt0-WdN9HwK8H0Wl8cjrVOLSBSTVzoAbVySwfoUvGl4LWwc6-vl5U8tjmzp2EOCM65zZg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Consequences_of_an_exotic_definition_for_P_NP_q","translated_slug":"","page_count":11,"language":"en","content_type":"Work","summary":"We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.","owner":{"id":631545,"first_name":"Francisco Antonio","middle_initials":"","last_name":"Doria","page_name":"FranciscoDoria","domain_name":"ufrj","created_at":"2011-07-31T14:20:54.461-07:00","display_name":"Francisco Antonio Doria","url":"https://ufrj.academia.edu/FranciscoDoria"},"attachments":[{"id":98570853,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/98570853/thumbnails/1.jpg","file_name":"AMC7887page.pdf","download_url":"https://www.academia.edu/attachments/98570853/download_file","bulk_download_file_name":"Consequences_of_an_exotic_definition_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/98570853/AMC7887page-libre.pdf?1676212326=\u0026response-content-disposition=attachment%3B+filename%3DConsequences_of_an_exotic_definition_for.pdf\u0026Expires=1743333191\u0026Signature=f6lPBIanDZLuY-xF66BEk8kb7L4iBVm7EhMSq-~lukVKnsQ9IpmwM0lqtV1gbo37WVlq2ISM7q3a8J-l4cXMT13mi1ej1FNIDZt0av-jE167rWwqgJxhyGSiEpfFVhhh8mEwt~ZHyE~7haqxczez8UdJGxt6hfjbWxoJ1ZfRiQg6piv1zgx~ZRe-nqejigFSh8p2D6KHQpFM~4pyrQnbNiSlkaydXBVTlrJVFgRnCxSlUjJNq4RAAt8i4l70ra7-BJ~C16CWrjVQEU4BKtt0-WdN9HwK8H0Wl8cjrVOLSBSTVzoAbVySwfoUvGl4LWwc6-vl5U8tjmzp2EOCM65zZg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":28911650,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.5882\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762492-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762491"><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/96762491/Baker_Gill_Solovay_set_of_polynomial_Turing"><img alt="Research paper thumbnail of Baker–Gill–Solovay set of polynomial Turing" class="work-thumbnail" src="https://attachments.academia-assets.com/98570854/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/96762491/Baker_Gill_Solovay_set_of_polynomial_Turing">Baker–Gill–Solovay set of polynomial Turing</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove here a lemma that connects some properties of the so-called "counterexample function" to...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove here a lemma that connects some properties of the so-called "counterexample function" to the P = N P conjecture over the Baker-Gill-Solovay set of polynomial Turing machines to the behavior of the same function "at large," over the set of all polynomial Turing machines.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c7faad172cd03a9bf41e4c4889cb0401" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570854,"asset_id":96762491,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570854/download_file?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="96762491"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762491"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762491; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762491-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762489"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/96762489/On_Teitler_s_higher_spin_field_equations"><img alt="Research paper thumbnail of On Teitler’s higher-spin field equations" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title">On Teitler’s higher-spin field equations</div><div class="wp-workCard_item"><span>Lettere Al Nuovo Cimento Series 2</span><span>, 1977</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96762489"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762489"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762489; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762489]").text(description); $(".js-view-count[data-work-id=96762489]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762489; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762489']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762489-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762487"><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/96762487/On_the_O_Donnell_Algorithm_for_NP_Complete_Problems"><img alt="Research paper thumbnail of On the O’Donnell Algorithm for NP-Complete Problems" class="work-thumbnail" src="https://attachments.academia-assets.com/98570857/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/96762487/On_the_O_Donnell_Algorithm_for_NP_Complete_Problems">On the O’Donnell Algorithm for NP-Complete Problems</a></div><div class="wp-workCard_item"><span>Review of Behavioral Economics</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If...</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 present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If P < N P is proved in a theory with greater "provability strength" than Primitive Recursive Arithmetic, the O'Donnell algorithm turns out to be almost polynomial. We elaborate on how close to polynomial it might be. As an application, we show that follows from Maymin's theorem on efficient markets that, given our metamathematical condition above, there are "almost efficient" markets (that is to say, markets where information about their operation is known in almost polynomial time).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a31d259e320db5b6f368b6cc0374b79b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570857,"asset_id":96762487,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570857/download_file?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="96762487"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762487"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762487; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762487]").text(description); $(".js-view-count[data-work-id=96762487]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762487; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762487']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "a31d259e320db5b6f368b6cc0374b79b" } } $('.js-work-strip[data-work-id=96762487]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762487,"title":"On the O’Donnell Algorithm for NP-Complete Problems","translated_title":"","metadata":{"publisher":"Now Publishers","grobid_abstract":"We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762487-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762485"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/96762485/Equations_for_a_spin_two_field_from_a_Dirac_like_equation"><img alt="Research paper thumbnail of Equations for a spin-two field from a Dirac-like equation" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title">Equations for a spin-two field from a Dirac-like equation</div><div class="wp-workCard_item"><span>Lettere Al Nuovo Cimento Series 2</span><span>, 1973</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96762485"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762485"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762485; 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We see that they describe other fields besides the. usual gauge fields, and impose certain degeneracies on the fields over a bifurcation domain.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6fcc4e850e600ca848cae3ddb25a7be5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570851,"asset_id":96762470,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570851/download_file?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="96762470"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762470"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762470; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762470]").text(description); $(".js-view-count[data-work-id=96762470]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762470; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762470']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "6fcc4e850e600ca848cae3ddb25a7be5" } } $('.js-work-strip[data-work-id=96762470]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762470,"title":"Dirac-Like Equations for Gauge Fields","translated_title":"","metadata":{"publisher":"Oxford University Press (OUP)","ai_title_tag":"Dirac-Like Equations for Gauge Field Theories","grobid_abstract":"We construct Dirac-like equations on a principal bundle over spacetime which is also the setting for the standard gauge field theories. 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We then examine the meaning of set-theoretic genericity for manifolds that underlie the Einstein equations. A physical interpretation is finally offered for those set-theoretically generic manifolds in gravitational theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8cf2120f81d006bbd92e885e2bb6a06" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570852,"asset_id":96762469,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570852/download_file?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="96762469"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762469"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762469; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762469]").text(description); $(".js-view-count[data-work-id=96762469]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762469; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762469']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "b8cf2120f81d006bbd92e885e2bb6a06" } } $('.js-work-strip[data-work-id=96762469]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762469,"title":"A Suppes predicate for general relativity and set-theoretically generic spacetimes","translated_title":"","metadata":{"publisher":"Springer Nature","grobid_abstract":"We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general relativity based on a Suppes predicate. 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Heretic viewpoints. </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="1028034"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="1028034"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 1028034; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=1028034]").text(description); $(".js-view-count[data-work-id=1028034]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 1028034; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='1028034']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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" } } $('.js-work-strip[data-work-id=1028034]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":1028034,"title":"Goedel's Way","translated_title":"","metadata":{"abstract":"My book with Greg Chaitin and Newton da Costa. 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","owner":{"id":631545,"first_name":"Francisco Antonio","middle_initials":"","last_name":"Doria","page_name":"FranciscoDoria","domain_name":"ufrj","created_at":"2011-07-31T14:20:54.461-07:00","display_name":"Francisco Antonio Doria","url":"https://ufrj.academia.edu/FranciscoDoria"},"attachments":[],"research_interests":[],"urls":[{"id":140387,"url":"http://www.taylorandfrancis.com/books/details/9780415690850/"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-1028034-figures'); } }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="94543" id="papers"><div class="js-work-strip profile--work_container" data-work-id="96762497"><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/96762497/The_Map_and_the_Territory"><img alt="Research paper thumbnail of The Map and the Territory" class="work-thumbnail" src="https://attachments.academia-assets.com/98570856/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/96762497/The_Map_and_the_Territory">The Map and the Territory</a></div><div class="wp-workCard_item"><span>The Frontiers Collection</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Science is a constructed narrative of the natural world based on information gathering and its su...</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">Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. In this essay, we develop a novel approach to the epistemic foundations of the scientific narrative, as based on our experiential interactions with the natural world. We first review some of the basic aspects of both Bayesian statistics and Shannon's information theory as applied to the construction of meaningful conceptualization of the natural world. This conceptualization is rendered through the maps we construct of the world based on our limited knowledge of reality. We propose a path from experience to information and physics based on the notion that information is experience that induces change in an Epistemic Agent (EA): the change may be local and focused to a minor aspect of reality or it may be broad and worldview-changing. We illustrate our approach through an analysis of a measure of spatial complexity proposed by one of us called Configuration Entropy (CE), and establish a link between experience at the cognitive level and information content, showing that the CE is a quantitative measure of how much information in spatial-complexity the external world hides from an EA. All philosophy is based on two things only: curiosity and poor eyesight. The trouble is, we want to know more than we can see. Bernard le Bovier de Fontenelle a To appear in Map and Territory-Exploring the Foundations of Science, Thought and Reality, ed.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1c6d514ffb72831b007a64604eb6a43b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570856,"asset_id":96762497,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570856/download_file?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="96762497"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762497"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762497; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762497]").text(description); $(".js-view-count[data-work-id=96762497]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762497; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762497']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "1c6d514ffb72831b007a64604eb6a43b" } } $('.js-work-strip[data-work-id=96762497]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762497,"title":"The Map and the Territory","translated_title":"","metadata":{"publisher":"Springer International Publishing","ai_title_tag":"From Experience to Information: The Epistemic Foundations of Science","grobid_abstract":"Science is a constructed narrative of the natural world based on information gathering and its subsequent analysis. 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We will consider specific examples of undecidable sentences in mathematics, physics and economics. 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We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.","publisher":"Springer International Publishing","publication_date":{"day":null,"month":null,"year":2016,"errors":{}},"publication_name":"Space, Time and the Limits of Human Understanding"},"translated_abstract":"We show how widespread are metamathematical phenomena in mathematics and in the sciences which rely on mathematics. We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.","internal_url":"https://www.academia.edu/96762495/G%C3%B6del_Incompleteness_and_the_Empirical_Sciences","translated_internal_url":"","created_at":"2023-02-12T05:58:26.365-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":631545,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"Gödel_Incompleteness_and_the_Empirical_Sciences","translated_slug":"","page_count":null,"language":"en","content_type":"Work","summary":"We show how widespread are metamathematical phenomena in mathematics and in the sciences which rely on mathematics. We will consider specific examples of undecidable sentences in mathematics, physics and economics. Our presentation is informal; rigorous developments can be found in the references.","owner":{"id":631545,"first_name":"Francisco Antonio","middle_initials":"","last_name":"Doria","page_name":"FranciscoDoria","domain_name":"ufrj","created_at":"2011-07-31T14:20:54.461-07:00","display_name":"Francisco Antonio Doria","url":"https://ufrj.academia.edu/FranciscoDoria"},"attachments":[],"research_interests":[],"urls":[{"id":28911651,"url":"http://link.springer.com/content/pdf/10.1007/978-3-319-44418-5_35"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762495-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762492"><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/96762492/Consequences_of_an_exotic_definition_for_P_NP_q"><img alt="Research paper thumbnail of Consequences of an exotic definition for P NP q" class="work-thumbnail" src="https://attachments.academia-assets.com/98570853/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/96762492/Consequences_of_an_exotic_definition_for_P_NP_q">Consequences of an exotic definition for P NP q</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equi...</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 introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b96003029bd2e84d81eb0a3a2761b4b5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570853,"asset_id":96762492,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570853/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="96762492"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762492"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762492; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762492]").text(description); $(".js-view-count[data-work-id=96762492]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762492; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762492']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "b96003029bd2e84d81eb0a3a2761b4b5" } } $('.js-work-strip[data-work-id=96762492]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762492,"title":"Consequences of an exotic definition for P NP q","translated_title":"","metadata":{"abstract":"We introduce a formal sentence noted P NPŠ F (the ‘‘exotic definition’’) that is intuitively equivalent to P NP; however P NP and P NPŠ F may not be equivalent in ZFC for some choices of F. 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Again for some F we show that P NPŠ F is consistent with ZFC, and so is the equivalence P NPŠ F $P NPŠ. We finally derive a consistency result for P NP itself.","owner":{"id":631545,"first_name":"Francisco Antonio","middle_initials":"","last_name":"Doria","page_name":"FranciscoDoria","domain_name":"ufrj","created_at":"2011-07-31T14:20:54.461-07:00","display_name":"Francisco Antonio Doria","url":"https://ufrj.academia.edu/FranciscoDoria"},"attachments":[{"id":98570853,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/98570853/thumbnails/1.jpg","file_name":"AMC7887page.pdf","download_url":"https://www.academia.edu/attachments/98570853/download_file","bulk_download_file_name":"Consequences_of_an_exotic_definition_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/98570853/AMC7887page-libre.pdf?1676212326=\u0026response-content-disposition=attachment%3B+filename%3DConsequences_of_an_exotic_definition_for.pdf\u0026Expires=1743333191\u0026Signature=f6lPBIanDZLuY-xF66BEk8kb7L4iBVm7EhMSq-~lukVKnsQ9IpmwM0lqtV1gbo37WVlq2ISM7q3a8J-l4cXMT13mi1ej1FNIDZt0av-jE167rWwqgJxhyGSiEpfFVhhh8mEwt~ZHyE~7haqxczez8UdJGxt6hfjbWxoJ1ZfRiQg6piv1zgx~ZRe-nqejigFSh8p2D6KHQpFM~4pyrQnbNiSlkaydXBVTlrJVFgRnCxSlUjJNq4RAAt8i4l70ra7-BJ~C16CWrjVQEU4BKtt0-WdN9HwK8H0Wl8cjrVOLSBSTVzoAbVySwfoUvGl4LWwc6-vl5U8tjmzp2EOCM65zZg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":28911650,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.92.5882\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") if (false) { Aedu.setUpFigureCarousel('profile-work-96762492-figures'); } }); </script> <div class="js-work-strip profile--work_container" data-work-id="96762491"><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/96762491/Baker_Gill_Solovay_set_of_polynomial_Turing"><img alt="Research paper thumbnail of Baker–Gill–Solovay set of polynomial Turing" class="work-thumbnail" src="https://attachments.academia-assets.com/98570854/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/96762491/Baker_Gill_Solovay_set_of_polynomial_Turing">Baker–Gill–Solovay set of polynomial Turing</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove here a lemma that connects some properties of the so-called "counterexample function" to...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove here a lemma that connects some properties of the so-called "counterexample function" to the P = N P conjecture over the Baker-Gill-Solovay set of polynomial Turing machines to the behavior of the same function "at large," over the set of all polynomial Turing machines.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="c7faad172cd03a9bf41e4c4889cb0401" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570854,"asset_id":96762491,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570854/download_file?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="96762491"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762491"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762491; 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If...</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 present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. If P < N P is proved in a theory with greater "provability strength" than Primitive Recursive Arithmetic, the O'Donnell algorithm turns out to be almost polynomial. We elaborate on how close to polynomial it might be. As an application, we show that follows from Maymin's theorem on efficient markets that, given our metamathematical condition above, there are "almost efficient" markets (that is to say, markets where information about their operation is known in almost polynomial time).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a31d259e320db5b6f368b6cc0374b79b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570857,"asset_id":96762487,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570857/download_file?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="96762487"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762487"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762487; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762487]").text(description); $(".js-view-count[data-work-id=96762487]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762487; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762487']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "a31d259e320db5b6f368b6cc0374b79b" } } $('.js-work-strip[data-work-id=96762487]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762487,"title":"On the O’Donnell Algorithm for NP-Complete Problems","translated_title":"","metadata":{"publisher":"Now Publishers","grobid_abstract":"We present and discuss the O'Donnell 1979 algorithm for the solution of N P-complete problems. 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We then state some undecidability and incompleteness results in classical analysis that lead to the explicit construction of expressions for characteristic functions in all complete arithmetical degrees. Out of those results we show that for any degree there are corresponding ‘meaningful’ unsolvable problems in</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="96762474"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762474"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762474; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762474]").text(description); $(".js-view-count[data-work-id=96762474]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762474; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762474']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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" } } $('.js-work-strip[data-work-id=96762474]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762474,"title":"Suppes Predicates and the Construction of Unsolvable Problems in the Axiomatized Sciences","translated_title":"","metadata":{"abstract":"We first review our previous work on Suppes predicates and the axiomatization of the empirical sciences. 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We then state some undecidability and incompleteness results in classical analysis that lead to the explicit construction of expressions for characteristic functions in all complete arithmetical degrees. 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We see that they describe other fields besides the. usual gauge fields, and impose certain degeneracies on the fields over a bifurcation domain.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6fcc4e850e600ca848cae3ddb25a7be5" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570851,"asset_id":96762470,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570851/download_file?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="96762470"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762470"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762470; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762470]").text(description); $(".js-view-count[data-work-id=96762470]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762470; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762470']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "6fcc4e850e600ca848cae3ddb25a7be5" } } $('.js-work-strip[data-work-id=96762470]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762470,"title":"Dirac-Like Equations for Gauge Fields","translated_title":"","metadata":{"publisher":"Oxford University Press (OUP)","ai_title_tag":"Dirac-Like Equations for Gauge Field Theories","grobid_abstract":"We construct Dirac-like equations on a principal bundle over spacetime which is also the setting for the standard gauge field theories. 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We then examine the meaning of set-theoretic genericity for manifolds that underlie the Einstein equations. A physical interpretation is finally offered for those set-theoretically generic manifolds in gravitational theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b8cf2120f81d006bbd92e885e2bb6a06" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570852,"asset_id":96762469,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570852/download_file?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="96762469"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762469"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762469; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762469]").text(description); $(".js-view-count[data-work-id=96762469]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762469; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762469']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "b8cf2120f81d006bbd92e885e2bb6a06" } } $('.js-work-strip[data-work-id=96762469]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762469,"title":"A Suppes predicate for general relativity and set-theoretically generic spacetimes","translated_title":"","metadata":{"publisher":"Springer Nature","grobid_abstract":"We summarize ideas from Zermelo-Fraenkel set theory up to an axiomatic treatment for general relativity based on a Suppes predicate. 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Their relation to forcing is also dealt with. 0 1995 John Wiiviley & Sons, Inc.</span></div><div class="wp-workCard_item"><div class="carousel-container carousel-container--sm" id="profile-work-96762468-figures"><div class="prev-slide-container js-prev-button-container"><button aria-label="Previous" class="carousel-navigation-button js-profile-work-96762468-figures-prev"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_back_ios</span></button></div><div class="slides-container js-slides-container"><figure class="figure-slide-container"><a href="https://www.academia.edu/figures/21744885/figure-1-example-let-us-be-given-the-following-infinite"><img alt="Example 5.6. Let us be given the following infinite denumer- able family A(m) of polynomial dynamical systems over Z, parametrized by ,,, m € w, and defined on an adequate Rx M: " class="figure-slide-image" src="https://figures.academia-assets.com/98570848/figure_001.jpg" /></a></figure></div><div class="next-slide-container js-next-button-container"><button aria-label="Next" class="carousel-navigation-button js-profile-work-96762468-figures-next"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">arrow_forward_ios</span></button></div></div></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6738de40f5afa7866bff4e093d0972bd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":98570848,"asset_id":96762468,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/98570848/download_file?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="96762468"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="96762468"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 96762468; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=96762468]").text(description); $(".js-view-count[data-work-id=96762468]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 96762468; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='96762468']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "6738de40f5afa7866bff4e093d0972bd" } } $('.js-work-strip[data-work-id=96762468]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":96762468,"title":"Gödel incompleteness, explicit expressions for complete arithmetic degrees and applications","translated_title":"","metadata":{"ai_title_tag":"Incompleteness in Real Analysis and Applications","grobid_abstract":"We summarize in a n intuitiue vein a few concepts froin recursion theory and fi-om the theory ofjormal systems and then state and comment our recent 1-esults on the incoinpleteness of elementary real analysis and its consequences. 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We define a free market to be a market where private ownership is positively valued by market members. In an economy with zero transaction costs, if the market is algorithmically complete, ownership will be worthless. Accordingly, the market can be either free or complete, but not both. 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