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{"work":{"id":21480115,"created_at":"2016-02-02T14:51:45.616-08:00","from_world_paper_id":147945206,"updated_at":"2025-01-12T22:05:00.187-08:00","_data":{"ai_abstract":"This chapter explores the proof-theoretic foundations of first-order arithmetic, emphasizing the significance of these foundational theories in mathematics. It discusses various axiomatizable fragments of first-order arithmetic, their strengths, and crucial concepts like incompleteness theorems and provably total functions. The chapter also references important literature in the field and highlights the necessity of understanding sequent calculus and cut-elimination for grasping key results in proof theory.","publication_date":"1998,,","publication_name":"Studies in Logic and the Foundations of Mathematics"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"First-Order Proof Theory of Arithmetic","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true,"seo_quality":null}}["work"]; window.loswp.workCoauthors = [5937540]; 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'; window.userInChina = "false";</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":41904055,"attachmentType":"pdf"}"><img alt="First page of “First-Order Proof Theory of Arithmetic”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/41904055/mini_magick20190218-19779-6b90yx.png?1550516551" /><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">First-Order Proof Theory 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="5937540" href="https://ucsd.academia.edu/SamBuss"><img alt="Profile image of Sam Buss" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/5937540/124686197/114045079/s65_sam.buss.jpeg" />Sam Buss</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1998, Studies in Logic and the Foundations of Mathematics</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">70 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 = 21480115; 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It discusses various axiomatizable fragments of first-order arithmetic, their strengths, and crucial concepts like incompleteness theorems and provably total functions. The chapter also references important literature in the field and highlights the necessity of understanding sequent calculus and cut-elimination for grasping key results in proof theory.</p></div></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="17065648" 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/17065648/Fragments_of_arithmetic">Fragments 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="196571" href="https://cmu.academia.edu/WilfriedSieg">Wilfried Sieg</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Pure and Applied Logic, 1985</p><p class="ds-related-work--abstract ds2-5-body-sm">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-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":"Fragments of arithmetic","attachmentId":42334579,"attachmentType":"pdf","work_url":"https://www.academia.edu/17065648/Fragments_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/17065648/Fragments_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="1" 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="2" data-entity-id="53141370" 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/53141370/On_Certain_Axiomatizations_of_Arithmetic_of_Natural_and_Integer_Numbers">On Certain Axiomatizations of Arithmetic of Natural and Integer Numbers</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="48364096" href="https://uksw.academia.edu/UrszulaWS">Urszula Wybraniec-Skardowska</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Axioms</p><p class="ds-related-work--abstract ds2-5-body-sm">The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two different ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relation of inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and propos...</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 Certain Axiomatizations of Arithmetic of Natural and Integer Numbers","attachmentId":70067696,"attachmentType":"pdf","work_url":"https://www.academia.edu/53141370/On_Certain_Axiomatizations_of_Arithmetic_of_Natural_and_Integer_Numbers","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/53141370/On_Certain_Axiomatizations_of_Arithmetic_of_Natural_and_Integer_Numbers"><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="3" data-entity-id="92756599" 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/92756599/Philosophy_of_Arithmetic">Philosophy 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="795663" href="https://utrgv.academia.edu/MelisaVivanco">Melisa Vivanco</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Melisa Vivanco, 2023</p><p class="ds-related-work--abstract ds2-5-body-sm">Some of the most influential programs in the philosophy of mathematics started from the philosophical study of natural numbers. On the one hand, our arithmetic intuitions appear earlier and more direct than other mathematical (and non-mathematical) intuitions. On the other hand, while arithmetic admits one of the first axiomatizations with wide acceptance within the mathematical practice, the study of natural numbers sets a methodological precedent that will later seek to be replicated in other areas, in particular, in the study of the most complex numerical structures. This course will address the main issues in the philosophical discussion on arithmetic. Among these topics are the ideas of the various classical doctrines on the foundations of arithmetic, from the milestone of Gödel’s incompleteness theorems to recent doctrines on the semantics of numerical expressions and arithmetic sentences. The class will cover debates about metaphysics and the epistemology of numbers and arithmetic truths.</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":"Philosophy of Arithmetic","attachmentId":95681402,"attachmentType":"pdf","work_url":"https://www.academia.edu/92756599/Philosophy_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/92756599/Philosophy_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="4" data-entity-id="102800636" 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/102800636/On_Certain_Extentions_of_the_Arithmetic_of_Addition_of_Natural_Numbers">On Certain Extentions of the Arithmetic of Addition of Natural Numbers</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="62823989" href="https://moscowstate.academia.edu/AlexeySemenov">Alexey Semenov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematics of the USSR – Izvestia. 15:2, 1980</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper the problems of expressibility and decidability are studied for elementary theories obtained by extending the arithmetic of order and the arithmetic of addition of natural numbers. Results are obtained on the decidability and undecidability of elementary theories of concrete structures of the form ⟨N;+,P⟩, where P is a fixed monadic predicate, as well as results on the class of sets definable in the theory T⟨N;+,λx,∃y(x=dy)⟩.</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 Certain Extentions of the Arithmetic of Addition of Natural Numbers","attachmentId":102974238,"attachmentType":"pdf","work_url":"https://www.academia.edu/102800636/On_Certain_Extentions_of_the_Arithmetic_of_Addition_of_Natural_Numbers","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/102800636/On_Certain_Extentions_of_the_Arithmetic_of_Addition_of_Natural_Numbers"><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="58396482" 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/58396482/Overspill_and_fragments_of_arithmetic">Overspill and fragments 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="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 arithmetic","attachmentId":72828028,"attachmentType":"pdf","work_url":"https://www.academia.edu/58396482/Overspill_and_fragments_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/58396482/Overspill_and_fragments_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="541142" 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/541142/Fragments_of_first_and_second_order_arithmetic_and_length_of_proofs">Fragments of first and second order arithmetic and length of proofs</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="411030" href="https://unsw.academia.edu/AleksandarIgnjatovic">Aleksandar Ignjatovic</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1990</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":"Fragments of first and second order arithmetic and length of proofs","attachmentId":2698948,"attachmentType":"pdf","work_url":"https://www.academia.edu/541142/Fragments_of_first_and_second_order_arithmetic_and_length_of_proofs","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/541142/Fragments_of_first_and_second_order_arithmetic_and_length_of_proofs"><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="78168085" 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/78168085/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="81344651" href="https://independent.academia.edu/CDD9">CD D</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":85310276,"attachmentType":"pdf","work_url":"https://www.academia.edu/78168085/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/78168085/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="8" 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="9" data-entity-id="118165086" 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/118165086/On_some_formalized_conservation_results_in_arithmetic">On some formalized conservation results in 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="39297879" href="https://independent.academia.edu/PClote">P. Clote</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Archive for Mathematical Logic, 1990</p><p class="ds-related-work--abstract ds2-5-body-sm">IX. and B2~, are well known fragments of first-order arithmetic with induction and collection for S. formulas respectively; IX ~ and BS ~ are their second-order counterparts. 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":113855409,"attachmentType":"pdf","work_url":"https://www.academia.edu/118165086/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/118165086/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" 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":41904055,"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":41904055,"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_41904055" 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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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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