Results 11 to 20 of about 86 (68)
Minimal models of Heyting arithmetic [PDF]
Journal of Symbolic Logic, 1997 In this paper, we give a constructive nonstandard model of intuitionistic arithmetic (Heyting arithmetic). We present two axiomatisations of the model: one finitary and one infinitary variant. Using the model these axiomatisations are proven to be conservative over ordinary intuitionistic arithmetic. The definition of the model along with the proofs of
Moerdijk, I., Palmgren, E.
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Propositional Logics of Closed and Open Substitutions over Heyting's Arithmetic [PDF]
Notre Dame Journal of Formal Logic, 2006 In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov's Arithmetic, that is, Heyting's Arithmetic plus Markov's principle plus Extended Church's ...
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Interactive Realizability for second-order Heyting arithmetic with EM1 and SK1 [PDF]
Mathematical Structures in Computer Science, 2013 We introduce a realizability semantics based on interactive learning for full second-order Heyting arithmetic with excluded middle and Skolem axioms over Σ10-formulas. Realizers are written in a classical version of Girard's System$\mathsf{F}$and can be viewed as programs that learn by interacting with the environment. We show that the realizers of any
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Noûs, Volume 58, Issue 2, Page 306-332, June 2024.Abstract Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal ...
Edward N. Zalta
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Weyl and two kinds of potential domains
Noûs, Volume 58, Issue 2, Page 409-430, June 2024.Abstract According to Weyl, “‘inexhaustibility’ is essential to the infinite”. However, he distinguishes two kinds of inexhaustible, or merely potential, domains: those that are “extensionally determinate” and those that are not. This article clarifies Weyl's distinction and explains its enduring logical and philosophical significance.
Laura Crosilla, Øystein Linnebo
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On the completenes principle: A study of provability in heyting's arithmetic and extensions
Annals of Mathematical Logic, 1982 AbstractIn this paper extensions of HA are studied that prove their own completeness, i.e. they prove A → □ A, where □ is interpreted as provability in the theory itself. Motivation is three-fold: (1) these theories are thought to have some intrinsic interest, (2) they are a tool for producing and studying provability principles, (3) they can be used ...
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Modern perspectives in Proof Theory. [PDF]
Philos Trans A Math Phys Eng Sci, 2023 Aguilera JP, Pakhomov F, Weiermann A.
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Ordinal analysis and the set existence property for intuitionistic set theories. [PDF]
Philos Trans A Math Phys Eng Sci, 2023 Rathjen M.
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Frege on intuition and objecthood in projective geometry. [PDF]
Synthese, 2021 Eder G.
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Intuitionistic fixed point theories over Heyting arithmetic
, 2010 In this paper we show that an intuitionistic theory for fixed points is conservative over the Heyting arithmetic with respect to a certain class of formulas. This extends partly the result of mine. The proof is inspired by the quick cut-elimination due to G. Mints.
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