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analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Mint ; each has been shown to be of considerable interest for both mathematical practice and me\u0026mathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems.","publication_date":"1985,,","publication_name":"Annals of Pure and Applied Logic","grobid_abstract_attachment_id":"42334579"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Fragments of arithmetic","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [196571]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "control"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":42334579,"attachmentType":"pdf"}"><img alt="First page of “Fragments of arithmetic”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/42334579/mini_magick20190217-5556-dxwb3m.png?1550464940" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Fragments of arithmetic</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="196571" href="https://cmu.academia.edu/WilfriedSieg"><img alt="Profile image of Wilfried Sieg" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/196571/19778430/19618665/s65_wilfried.sieg.png" />Wilfried Sieg</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1985, Annals of Pure and Applied Logic</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">39 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 17065648; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=17065648"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">We establish by elementary proof-theoretic means the conservativeness of two subsystems of analysis over primitive recursive arithmetic. The one subsystem was introduced by Friedman [6], the other is a strengthened version of a theory of Mint ; each has been shown to be of considerable interest for both mathematical practice and me&mathematical investigations. The foundational significance of such conservation results is clear: they provide a direct finitist justification of the part of mathematical practice formalizable in these subsystems.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":42334579,"attachmentType":"pdf","workUrl":"https://www.academia.edu/17065648/Fragments_of_arithmetic"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":42334579,"attachmentType":"pdf","workUrl":"https://www.academia.edu/17065648/Fragments_of_arithmetic"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger"></div></div><div class="ds-signup-banner ds-signup-banner-simple-copy"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><h4 class="ds2-5-heading-serif-sm">Sign up to get access to over 50M papers</h4><button class="ds2-5-button ds2-5-button--inverse js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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RCA o is the well known fragment of second-order arithmetic with recursive comprehension; WKLo is RCA o plus weak K6nig's lemma. We first strengthen Harrington's conservation result by showing that WKLo + BS ~ is H~-conservative over RCAo + BX ~ Then we develop some model theory in WKLo and illustrate the use of formalized model theory by giving a relatively simple proof of the fact that 1X 1 proves BX n + 1 to be H, + 2-conservative over 127,. Finally, we present a proof-theoretic proof of the stronger fact that the H, + a conservation result is provable already in IA o + superexp. Thus 1S, + 1 proves 1-Con (BS,+ 1) and IA o + superexp proves Con (IS,)+-+Con(BX,+ 1).</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On some formalized conservation results in arithmetic","attachmentId":101956619,"attachmentType":"pdf","work_url":"https://www.academia.edu/101406073/On_some_formalized_conservation_results_in_arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/101406073/On_some_formalized_conservation_results_in_arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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data-collection-position="4" data-entity-id="58886653" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/58886653/The_Arithmetic_Hierarchy_Parikhs_Theorem_and_Related_Matters">The Arithmetic Hierarchy, Parikh's Theorem and Related Matters</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="46358647" href="https://helsinki.academia.edu/JulietteKennedy">Juliette Kennedy</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Arithmetic Hierarchy, Parikh's Theorem and Related Matters","attachmentId":73079808,"attachmentType":"pdf","work_url":"https://www.academia.edu/58886653/The_Arithmetic_Hierarchy_Parikhs_Theorem_and_Related_Matters","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/58886653/The_Arithmetic_Hierarchy_Parikhs_Theorem_and_Related_Matters"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="48462646" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/48462646/Completeness_theorems_incompleteness_theorems_and_models_of_arithmetic">Completeness theorems, incompleteness theorems and models of arithmetic</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="100282984" href="https://independent.academia.edu/KenMcAloon">Ken McAloon</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Transactions of the American Mathematical Society, 1978</p><p class="ds-related-work--abstract ds2-5-body-sm">Let & be a consistent extension of Peano arithmetic and let 6EJJ denote the set of TL°" consequences of &. Employing incompleteness theorems to generate independent formulas and completeness theorems to construct models, we build nonstandard models of SP"+2 m which the standard integers are A°+1-definable. We thus pinpoint induction axioms which are not provable in éE¡¡+2; in particular, we show that (parameter free) A?-induction is not provable in Primitive Recursive Arithmetic. Also, we give a solution of a problem of Gaifman on the existence of roots of diophantine equations in end extensions and answer questions about existentially complete models of 3^. Furthermore, it is shown that the proof of the Gödel Completeness Theorem cannot be formalized in 6E § and that the MacDowell-Specker Theorem fails for all truncated theories (£¡¡.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Completeness theorems, incompleteness theorems and models of arithmetic","attachmentId":67061152,"attachmentType":"pdf","work_url":"https://www.academia.edu/48462646/Completeness_theorems_incompleteness_theorems_and_models_of_arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/48462646/Completeness_theorems_incompleteness_theorems_and_models_of_arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="101258886" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/101258886/G%C3%B6dels_Second_Incompleteness_Theorem_for_General_Recursive_Arithmetic">Gödel's Second Incompleteness Theorem for General Recursive Arithmetic</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="268377356" href="https://independent.academia.edu/C%C4%91%C4%90">Cđ Đ</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1978</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Gödel's Second Incompleteness Theorem for General Recursive Arithmetic","attachmentId":101849559,"attachmentType":"pdf","work_url":"https://www.academia.edu/101258886/G%C3%B6dels_Second_Incompleteness_Theorem_for_General_Recursive_Arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/101258886/G%C3%B6dels_Second_Incompleteness_Theorem_for_General_Recursive_Arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="160314" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/160314/Predicative_foundations_of_arithmetic">Predicative foundations of arithmetic</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13693" href="https://stanford.academia.edu/SolomonFeferman">Solomon Feferman</a></div><p class="ds-related-work--abstract ds2-5-body-sm">Predicative mathematics in the sense originating with Poincaré and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithmetic itself. 1 It is the main purpose of this paper to show that this appearance is illusory: as will emerge, a predicatively acceptable axiomatization of the natural number system can be formulated, and both the existence of structures of the relevant type and the categoricity of the relevant axioms can be proved in a predicatively acceptable way.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Predicative foundations of\n arithmetic","attachmentId":68370,"attachmentType":"pdf","work_url":"https://www.academia.edu/160314/Predicative_foundations_of_arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/160314/Predicative_foundations_of_arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="65807298" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/65807298/On_the_limit_existence_principles_in_elementary_arithmetic_and_%CE%A3_0_n_consequences_of_theories">On the limit existence principles in elementary arithmetic and Σ 0 n-consequences of theories</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="80365520" href="https://uu.academia.edu/albertvisser">albert visser</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2005</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the arithmetical schema asserting that every eventually decreasing elementary recursive function has a limit. Some other related principles are also formulated. We establish their relationship with restricted parameter-free induction schemata. We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ2-consequences of IΣ1. Using these results we show that ILM is the logic of Π1-conservativity of any reasonable extension of parameter-free Π1-induction schema. This result, however, cannot be much improved: by adapting a theorem of D. Zambella and G. Mints we show that the logic of Π1-conservativity of primitive recursive arithmetic properly extends ILM. In the third part of the paper we give an ordinal classification of Σn-consequences of the standard fragments of Peano arithmetic in terms of reflection principles. This is interesting in view of the general program of ordinal analysis of theories, which in the most standard cas...</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the limit existence principles in elementary arithmetic and Σ 0 n-consequences of theories","attachmentId":77243717,"attachmentType":"pdf","work_url":"https://www.academia.edu/65807298/On_the_limit_existence_principles_in_elementary_arithmetic_and_%CE%A3_0_n_consequences_of_theories","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/65807298/On_the_limit_existence_principles_in_elementary_arithmetic_and_%CE%A3_0_n_consequences_of_theories"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="84812302" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/84812302/Provably_total_recursive_functions_and_MRDP_theorem_in_Basic_Arithmetic_and_its_extensions">Provably total recursive functions and MRDP theorem in Basic Arithmetic and its extensions</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="40855901" href="https://independent.academia.edu/MohammadArdeshir">Mohammad Ardeshir</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv: Logic, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">We study Basic Arithmetic, BA introduced by W. Ruitenburg. BA is an arithmetical theory based on basic logic which is weaker than intuitionistic logic. We show that the class of the provably recursive functions of BA is a proper sub-class of primitive recursive functions. Three extensions of BA, called BA+U, BA_c and EBA are investigated with relation to their provably recursive functions. It is shown that the provably recursive functions of these three extensions of BA are exactly primitive recursive functions. Moreover, among other things, it is shown that the well-known MRDP theorem doesn&#39;t hold in BA, BA+U, BA_c, but holds in EBA.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Provably total recursive functions and MRDP theorem in Basic Arithmetic and its extensions","attachmentId":89708431,"attachmentType":"pdf","work_url":"https://www.academia.edu/84812302/Provably_total_recursive_functions_and_MRDP_theorem_in_Basic_Arithmetic_and_its_extensions","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/84812302/Provably_total_recursive_functions_and_MRDP_theorem_in_Basic_Arithmetic_and_its_extensions"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":42334579,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":42334579,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_42334579" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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href="https://impan.academia.edu/ZofiaAdamowicz">Zofia Adamowicz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Symbolic Logic, 2016</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Existentially Closed Models in the Framework of Arithmetic","attachmentId":111561987,"attachmentType":"pdf","work_url":"https://www.academia.edu/115036275/Existentially_Closed_Models_in_the_Framework_of_Arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/115036275/Existentially_Closed_Models_in_the_Framework_of_Arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="12" data-entity-id="9727886" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/9727886/On_Arithmetic_Formulated_Connexively">On Arithmetic Formulated Connexively</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9896443" href="https://rpi.academia.edu/ThomasFerguson">Thomas M Ferguson</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Arithmetic Formulated 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href="https://www.academia.edu/117691154/On_the_optimality_of_conservation_results_for_local_reflection_in_arithmetic">On the optimality of conservation results for local reflection in arithmetic</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="300834999" href="https://independent.academia.edu/Andr%C3%A9sCoveloFranco">Andrés Covelo Franco</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Symbolic Logic, 2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the optimality of conservation results for local reflection in arithmetic","attachmentId":113483808,"attachmentType":"pdf","work_url":"https://www.academia.edu/117691154/On_the_optimality_of_conservation_results_for_local_reflection_in_arithmetic","alternativeTracking":true}"><span 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ds2-5-body-sm ds2-5-body-link" data-author-id="117828974" href="https://independent.academia.edu/JohnBurgess31">John Burgess</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Notre Dame Journal of Formal Logic, 1998</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Predicative Logic and Formal Arithmetic","attachmentId":110619161,"attachmentType":"pdf","work_url":"https://www.academia.edu/113731321/Predicative_Logic_and_Formal_Arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/113731321/Predicative_Logic_and_Formal_Arithmetic"><span 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The Reasoner, Vol (1) 8 p6-7</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="319497" href="https://independent.academia.edu/BhupinderSinghAnand">Bhupinder Singh Anand</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2007</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A c onstructive definition of the intuitive truth of the Axioms and Rules of Inference of Peano Arithmetic. 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data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/41133178/A_Proof_Theory_for_the_Logic_of_Provability_in_True_Arithmetic">A Proof Theory for the Logic of Provability in True Arithmetic</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="512336" href="https://mlit.academia.edu/HirohikoKushida%E4%B8%B2%E7%94%B0%E8%A3%95%E5%BD%A6">Hirohiko Kushida　串田裕彦</a></div><p class="ds-related-work--metadata ds2-5-body-xs">STUDIA LOGICA, vol.108(4), pp 857-875, 2020</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Proof Theory for the Logic of Provability in True 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href="https://www.academia.edu/36266879/On_the_Consistency_of_the_Arithmetic_System">On the Consistency of the Arithmetic System</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="36279391" href="https://independent.academia.edu/StepienLukasz">Lukasz T Stepien</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2017</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Consistency of the Arithmetic System","attachmentId":56172207,"attachmentType":"pdf","work_url":"https://www.academia.edu/36266879/On_the_Consistency_of_the_Arithmetic_System","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a 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href="https://independent.academia.edu/BhupinderSinghAnand">Bhupinder Singh Anand</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2012</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Some consequences of interpreting the associated logic of the rst-order Peano Arithmetic PA nitarily","attachmentId":112232364,"attachmentType":"pdf","work_url":"https://www.academia.edu/115973654/Some_consequences_of_interpreting_the_associated_logic_of_the_rst_order_Peano_Arithmetic_PA_nitarily","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/115973654/Some_consequences_of_interpreting_the_associated_logic_of_the_rst_order_Peano_Arithmetic_PA_nitarily"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="19" data-entity-id="12541822" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/12541822/Proving_consistency_of_equational_theories_in_bounded_arithmetic">Proving consistency of equational theories in bounded arithmetic</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="31440864" href="https://independent.academia.edu/ArnoldBeckmann">Arnold Beckmann</a></div><p class="ds-related-work--metadata ds2-5-body-xs">The Journal of Symbolic Logic, 2002</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Proving consistency of equational theories in bounded arithmetic","attachmentId":46102380,"attachmentType":"pdf","work_url":"https://www.academia.edu/12541822/Proving_consistency_of_equational_theories_in_bounded_arithmetic","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/12541822/Proving_consistency_of_equational_theories_in_bounded_arithmetic"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="20" data-entity-id="58396482" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/58396482/Overspill_and_fragments_of_arithmetic">Overspill and fragments of arithmetic</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="30022870" href="https://independent.academia.edu/CostasDimitrakopoulos">Costas Dimitrakopoulos</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Archive for Mathematical Logic, 1989</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Overspill and fragments of 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href="https://www.academia.edu/70642516/Bolet%C3%ADn_de_Matem%C3%A1ticas_Nueva_Serie_Volumen_IV_1997_pp_73_84_RECURSION_IN_SECOND_ORDER_BOUNDED_ARITHMETIC">Boletín de Matemáticas Nueva Serie, Volumen IV (1997), pp. 73-84 RECURSION IN SECOND ORDER BOUNDED ARITHMETIC</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="148162601" href="https://unal.academia.edu/RodrigoDeCastro">Rodrigo De Castro</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2016</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Boletín de Matemáticas Nueva Serie, Volumen IV (1997), pp. 73-84 RECURSION IN SECOND ORDER BOUNDED ARITHMETIC","attachmentId":80309057,"attachmentType":"pdf","work_url":"https://www.academia.edu/70642516/Bolet%C3%ADn_de_Matem%C3%A1ticas_Nueva_Serie_Volumen_IV_1997_pp_73_84_RECURSION_IN_SECOND_ORDER_BOUNDED_ARITHMETIC","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/70642516/Bolet%C3%ADn_de_Matem%C3%A1ticas_Nueva_Serie_Volumen_IV_1997_pp_73_84_RECURSION_IN_SECOND_ORDER_BOUNDED_ARITHMETIC"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="22" data-entity-id="60450514" data-sort-order="default"><a 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