Results 51 to 60 of about 166,162,676 (139)
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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Initial segments and end-extensions of models of arithmetic [PDF]
, 2010 This thesis is organized into two independent parts. In the first part, we extend the recent work on generic cuts by Kaye and the author. The focus here is the properties of the pairs (M, I) where I is a generic cut of a model M.
Wong, Tin Lok
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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 automorphisms of models of Peano arithmetic
, 2004 When studying the automorphism group Aut(M) of a model M, one is interested to what extent M is recoverable from Aut(M). We show that if M is a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if a maximal open subgroup ...
Nurkhaidarov, Ermek S
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COMPUTABLE QUOTIENT PRESENTATIONS OF MODELS OF ARITHMETIC AND SET THEORY (Mathematical Logic and Its Applications) [PDF]
, 2017 We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory.
Hamkins, Joel David +1 more
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On the Structure of Nonstandard Models of Arithmetic [PDF]
Proceedings of the American Mathematical Society, 1971 openaire +2 more sources
The Fine Structure Theory of Nonstandard Models of Peano Arithmetic
This paper delves into the fine structure theory of nonstandard models of Peano Arithmetic (PA). Nonstandard models provide a rich landscape for exploring foundational issues in arithmetic, extending beyond the intuitive standard model of natural numbers.
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Non-standard discretization of biological models [PDF]
, 2015 We consider certain types of discretization schemes for differential equations with quadratic nonlinearities, which were introduced by Kahan, and considered in a broader setting by Mickens.
Towler, Kim, Hone, Andrew N.W.
core
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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