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href="https://independent.academia.edu/ZarkoMijajlovic"><img alt="Profile image of Zarko Mijajlovic" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Zarko Mijajlovic</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1983, Notre Dame Journal of Formal 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">9 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 = 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data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></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="27771727" 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/27771727/Internal_End_Extensions_of_Peano_Arithmetic_and_a_Problem_of_Gaifman">Internal End-Extensions of Peano Arithmetic and a Problem of Gaifman</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="34940590" href="https://anekdoty.academia.edu/LarryManevitz">Larry Manevitz</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of the London Mathematical Society, 1976</p><p class="ds-related-work--abstract ds2-5-body-sm">A well known result of M. Rabin states that the only existentially complete model of full arithmetic is the standard one. H. Gaifman [1], raised the parallel question for end-extensions of full arithmetic, i.e. does every non-standard model of full arithmetic have an end-extension in which a diophantine equation unsolvable in the original model has a solution. A. Wilkie provided a partial answer [4] when he proved that every countable model of P, Peano Arithmetic, has such an end-extension (which is in fact isomorphic to the original model).</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":"Internal End-Extensions of Peano Arithmetic and a Problem of Gaifman","attachmentId":48049579,"attachmentType":"pdf","work_url":"https://www.academia.edu/27771727/Internal_End_Extensions_of_Peano_Arithmetic_and_a_Problem_of_Gaifman","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/27771727/Internal_End_Extensions_of_Peano_Arithmetic_and_a_Problem_of_Gaifman"><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="115036275" 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/115036275/Existentially_Closed_Models_in_the_Framework_of_Arithmetic">Existentially Closed Models in the Framework 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="61300629" 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><p class="ds-related-work--abstract ds2-5-body-sm">We prove that the standard cut is definable in each existentially closed model of I Δ 0 +exp by a (parameter free) Π 1-formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic. 1. Introduction. This work was initially motivated by a gap in the proof of Corollary 1.3 of [2] providing a parameter free Π 1-definition of the standard cut, N, in each existentially closed (e.c.) model of I Δ 0 + exp. Our aim is to provide a correct proof of the above result and, use it to obtain an updated view of the theory of e.c. models of I Δ 0 +exp. Existentially closed models of arithmetic were investigated in the 1970's as a part of the efforts to get a full understanding of the model theory of existentially closed structures (existence of model completions and companion theories, finite and infinite forcing, etc.). The results obtained in the early 1970's by A. Robinson, J. Hirschfeld, D. C. Goldrei, A. Macintyre, and H. Simmons pointed out the most important property of e.c. models of sufficiently strong arithmetic theories: there exist formulas defining N in each such model. These results were not stated in their full generality. In the 1970's a systematic study of fragments of Peano arithmetic PA was still to come and the authors focused essentially on e.c. models of Π 2 (N) (thesetoftrueΠ 2-sentences) or of Π 2 (PA)(thesetofΠ 2 consequences of PA), and more generally on e.c. models of Π 2 (T B), where T B is any extension of Π 2 (PA). Regarding Π 2 (N), Robinson (see [14]) proved N to be Σ 3-definable in every e.c. model of Π 2 (N) and Hirschfeld (see [7]) improved Robinson's result obtaining a Σ 2-definition of N,or even aΠ 1-definition, if parameters are allowed. Hirschfeld also showed that these definitions are optimal (in terms of quantifier complexity) for e.c. models of Π 2 (N). As to Π 2 (T B), in [11] Macintyre and Simmons (see also [5]) extended Hirschfeld's Σ 2-definition of N to all e.c. models of Π 2 (T B) and showed that the parametric Π 1definition can be extended to those e.c. models of Π 2 (T B)inwhichtheΣ 1-definable elements are not cofinal. However, these definitions are not best possible, since there is no general result ruling out the possibility of a parameter free Π 1-definition of N valid in all e.c. models. As a matter of fact, such an optimal definition was Key words and phrases. fragments of Peano arithmetic, existentially closed models, turing degrees of arithmetic 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":"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-wsj-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-wsj-grid-card" data-collection-position="2" data-entity-id="110023571" 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/110023571/Expressibility_in_the_elementary_theory_of_recursively_enumerable_sets_with_realizability_logic">Expressibility in the elementary theory of recursively enumerable sets with realizability logic</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="267944" href="https://ut-ee.academia.edu/ReinPrank">Rein Prank</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Algebra and Logic, 1981</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":"Expressibility in the elementary theory of recursively enumerable sets with realizability logic","attachmentId":107970534,"attachmentType":"pdf","work_url":"https://www.academia.edu/110023571/Expressibility_in_the_elementary_theory_of_recursively_enumerable_sets_with_realizability_logic","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/110023571/Expressibility_in_the_elementary_theory_of_recursively_enumerable_sets_with_realizability_logic"><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="58396494" 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/58396494/On_end_extensions_of_models_of_subsystems_of_peano_arithmetic">On end extensions of models of subsystems of peano 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">Theoretical Computer Science, 2001</p><p class="ds-related-work--abstract ds2-5-body-sm">We survey results and problems concerning subsystems of Peano Arithmetic. In particular, we deal with end extensions of models of such theories. First, we discuss the results of Paris</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 end extensions of models of subsystems of peano arithmetic","attachmentId":72828053,"attachmentType":"pdf","work_url":"https://www.academia.edu/58396494/On_end_extensions_of_models_of_subsystems_of_peano_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/58396494/On_end_extensions_of_models_of_subsystems_of_peano_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="106012637" 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/106012637/Models_and_types_of_Peanos_arithmetic">Models and types of Peano's 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="6964329" href="https://columbia.academia.edu/HGaifman">Haim Gaifman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Mathematical Logic, 1976</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":"Models and types of Peano's arithmetic","attachmentId":105322539,"attachmentType":"pdf","work_url":"https://www.academia.edu/106012637/Models_and_types_of_Peanos_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/106012637/Models_and_types_of_Peanos_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="5" data-entity-id="80112894" 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/80112894/Provability_logic_models_within_models_in_Peano_Arithmetic">Provability logic: models within models in Peano 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="18337933" href="https://independent.academia.edu/AlessandroBerarducci">Alessandro Berarducci</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Bollettino dell'Unione Matematica Italiana</p><p class="ds-related-work--abstract ds2-5-body-sm">In 1994 Jech gave a model-theoretic proof of Gödel’s second incompleteness theorem for Zermelo–Fraenkel set theory in the following form: $${{\,\mathrm{\mathrm {ZF}}\,}}$$ ZF does not prove that $${{\,\mathrm{\mathrm {ZF}}\,}}$$ ZF has a model. Kotlarski showed that Jech’s proof can be adapted to Peano Arithmetic with the role of models being taken by complete consistent extensions. In this note we take another step in the direction of replacing proof-theoretic by model-theoretic arguments. We show, without the need of formalizing the proof of the completeness theorem within $${{\,\mathrm{\mathrm {PA}}\,}}$$ PA , that the existence of a model of $${{\,\mathrm{\mathrm {PA}}\,}}$$ PA of complexity $$\Sigma ^0_2$$ Σ 2 0 is independent of $${{\,\mathrm{\mathrm {PA}}\,}}$$ PA , where a model is identified with the set of formulas with parameters which hold in the model. Our approach is based on a new interpretation of the provability logic of Peano Arithmetic where $$\Box \phi $$ □ ϕ is ...</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":"Provability logic: models within models in Peano Arithmetic","attachmentId":86603343,"attachmentType":"pdf","work_url":"https://www.academia.edu/80112894/Provability_logic_models_within_models_in_Peano_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/80112894/Provability_logic_models_within_models_in_Peano_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="2405515" 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/2405515/On_the_Provability_Logic_of_Bounded_Arithmetic">On the Provability Logic of Bounded 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="41333" href="https://rug.academia.edu/RinekeVerbrugge">Rineke Verbrugge</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="18337933" href="https://independent.academia.edu/AlessandroBerarducci">Alessandro Berarducci</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Pure and Applied Logic, 1993</p><p class="ds-related-work--abstract ds2-5-body-sm">A. and R. Verbrugge, On the provability logic of bounded arithmetic, Annals of Pure and Applied Logic 61 (1993) 75-93.</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 Provability Logic of Bounded Arithmetic","attachmentId":50643683,"attachmentType":"pdf","work_url":"https://www.academia.edu/2405515/On_the_Provability_Logic_of_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/2405515/On_the_Provability_Logic_of_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-wsj-grid-card" data-collection-position="7" data-entity-id="85731506" 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/85731506/Definability_automorphisms_and_infinitary_languages">Definability, automorphisms, and infinitary languages</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="32902765" href="https://independent.academia.edu/DavidKueker">David Kueker</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Lecture Notes in Mathematics, 1968</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":"Definability, automorphisms, and infinitary languages","attachmentId":90341813,"attachmentType":"pdf","work_url":"https://www.academia.edu/85731506/Definability_automorphisms_and_infinitary_languages","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/85731506/Definability_automorphisms_and_infinitary_languages"><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="115973654" 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/115973654/Some_consequences_of_interpreting_the_associated_logic_of_the_rst_order_Peano_Arithmetic_PA_nitarily">Some consequences of interpreting the associated logic of the rst-order Peano Arithmetic PA nitarily</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="319497" 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><p class="ds-related-work--abstract ds2-5-body-sm">We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two essentially different ways: (a) in terms of algorithmic verifiabilty; and (b) in terms of algorithmic computability. We show that the classical Standard interpretation I_PA(N, Standard) of PA essentially defines the satisfaction and truth of the formulas of the first-order Peano Arithmetic PA in terms of algorithmic verifiability. It is accepted that this classical interpretation---in terms of algorithmic verifiabilty---cannot lay claim to be finitary; it does not lead to a finitary justification of the Axiom Schema of Finite Induction of PA from which we may conclude---in an intuitionistically unobjectionable manner---that PA is consistent. We now show that the PA-axioms---including the Axiom Schema of Finite Induction---are, however, algorithmically computable finitarily as satisfied / true under the Standard interpretation I_PA(N, Standard) of PA; and that the PA rules of inference do preserve algorithmically computable satisfiability / truth finitarily under the Standard interpretation I_PA(N, Standard). We conclude that the algorithmically computable PA-formulas can provide a finitary interpretation I_PA(N, Algorithmic) of PA from which we may classically conclude that PA is consistent in an intuitionistically unobjectionable manner. We define this interpretation, and show that if the associated logic is interpreted finitarily then (i) PA is categorical and (ii) Goedel's Theorem VI holds vacuously in PA since PA is consistent but not omega-consistent.</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-wsj-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-wsj-grid-card" data-collection-position="9" data-entity-id="54611074" 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/54611074/Degrees_of_insolubility_of_extensions_of_arithmetic_by_true_propositions">Degrees of insolubility of extensions of arithmetic by true propositions</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="65652877" href="https://independent.academia.edu/OOkunev">Oleg Okunev</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Russian Mathematical Surveys, 1988</p><p class="ds-related-work--abstract ds2-5-body-sm">By the degree of insolubility (or simply degree) d (T) of a theory Τwe mean the Turing degree of the set of Godel numbers of the theorems of Τ [1]. In this paper we solve the problem of the degrees of extensions of the arithmetic PA by true propositions. It follows from the classical theorems on insolubility that all these degrees are greater than or equal to O&#x27;• In this paper we prove that the set of these degrees coincides with the ideal/(0&#x27;)={a| O&#x27;C&quot;}· The main theorem also implies that every degree inKO) contains a theory of the class under ...</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":"Degrees of insolubility of extensions of arithmetic by true propositions","attachmentId":70893412,"attachmentType":"pdf","work_url":"https://www.academia.edu/54611074/Degrees_of_insolubility_of_extensions_of_arithmetic_by_true_propositions","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/54611074/Degrees_of_insolubility_of_extensions_of_arithmetic_by_true_propositions"><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":73891899,"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":73891899,"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_73891899" 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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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-related-work-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-related-work-sidebar-card" data-collection-position="6" data-entity-id="75026640" 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/75026640/Weak_Logical_Constants_and_Second_Order_Definability_of_the_Full_Strength_Logical_Constants">Weak Logical Constants and Second Order Definability of the Full-Strength Logical Constants</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="31712080" href="https://keio.academia.edu/MitsuhiroOkada">Mitsuhiro Okada</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of the Japan Association for Philosophy of Science, 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":"Weak 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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 definability theorem for first order logic","attachmentId":82401147,"attachmentType":"pdf","work_url":"https://www.academia.edu/74144835/A_definability_theorem_for_first_order_logic","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/74144835/A_definability_theorem_for_first_order_logic"><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="13" data-entity-id="12038087" 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class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 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 new principle in the interpretability logic of all reasonable arithmetical theories","attachmentId":113160838,"attachmentType":"pdf","work_url":"https://www.academia.edu/117255565/A_new_principle_in_the_interpretability_logic_of_all_reasonable_arithmetical_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-related-work-grid-card-view-pdf" href="https://www.academia.edu/117255565/A_new_principle_in_the_interpretability_logic_of_all_reasonable_arithmetical_theories"><span class="ds2-5-text-link__content">View 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data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Modal Logic of Consistency Assertions of Peano Arithmetic","attachmentId":109534497,"attachmentType":"pdf","work_url":"https://www.academia.edu/112245398/The_Modal_Logic_of_Consistency_Assertions_of_Peano_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/112245398/The_Modal_Logic_of_Consistency_Assertions_of_Peano_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="17" data-entity-id="20499209" 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