Results 1 to 10 of about 294 (99)
Cofinal extensions of nonstandard models of arithmetic.
Notre Dame Journal of Formal Logic, 1981 C Smorynski
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Privacy-Preserving Machine Learning With Fully Homomorphic Encryption for Deep Neural Network
IEEE Access, 2022 Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches.
Joon-Woo Lee +10 more
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Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století
Filosofický časopis, 2022 Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been
Haniková, Zuzana
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Satisfaction classes in nonstandard models of first-order arithmetic
, 2002 A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively ...
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A note on $\mathbb{Z}$ as a direct summand of nonstandard models of weak systems of arithmetic
, 2016 There are nonstandard models of normal open induction ($NOI$) for which $\mathbb{Z}$ is a direct summand of their additive group. We show that this is impossible for nonstandard models of $IE_2$.
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Steps Toward a Philosophy for Mathematicians. [PDF]
Math Intell, 2023 Fenstad JE.
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Human verifications: Computable with truth values outside logic. [PDF]
Proc Natl Acad Sci U S A, 2023 Johnson-Laird PN +2 more
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Constructive Nonstandard Models for Peano Arithmetic
This paper explores the notion of constructive nonstandard models for Peano Arithmetic (PA). While classical model theory provides a rich landscape of nonstandard models, their existence often relies on non-constructive principles such as the Axiom of Choice or the Compactness Theorem.
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On the Structure of Nonstandard Models of Arithmetic [PDF]
Proceedings of the American Mathematical Society, 1971 openaire +2 more sources
Destructibility and axiomatizability of Kaufmann models. [PDF]
Arch Math Log, 2022 Switzer CB.
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