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Every Countable Model of Arithmetic or Set Theory has a Pointwise-Definable End Extension [PDF]
KRITERION – Journal of Philosophy, 2022 According to the math tea argument, there must be real numbers that we cannot describe or define, because there are uncountably many real numbers, but only countably many definitions. And yet, the existence of pointwise-definable models of set theory, in
J. Hamkins
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EXTENSIONAL REALIZABILITY AND CHOICE FOR DEPENDENT TYPES IN INTUITIONISTIC SET THEORY [PDF]
Journal of Symbolic Logic (JSL), 2022 In [17], we introduced an extensional variant of generic realizability [22], where realizers act extensionally on realizers, and showed that this form of realizability provides inner models of $\mathsf {CZF}$ (constructive Zermelo–Fraenkel set theory ...
EMANUELE FRITTAION
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Social Science Research Network, 2022 The previous Part I of the paper (https://doi.org/10.33774/coe-2022-wlr02) discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the ...
Vasil Penchev
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Does Set Theory Really Ground Arithmetic Truth? [PDF]
Axioms, 2019 We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth. Our method is to emphasize the incomplete picture of both theories
Alfredo Roque Freire
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Ehrenfeucht's Lemma in Set Theory [PDF]
Notre Dame J. Formal Log., 2015 Ehrenfeucht’s lemma [Ehr73] asserts that whenever one element of a model of Peano arithmetic is definable from another, then they satisfy different types. We consider here the analogue of Ehrenfeucht’s lemma for models of set theory.
G. Fuchs, V. Gitman, J. Hamkins
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Journal of Applied Business and Economics, 2019 The focus of this article is on highlighting the principal results contained in the recently published e-book: An Introduction to Macroeconomic Models in Excel: A Data-Driven, Arithmetic Approach for Principles of Economics Students. The discussion below
M. Rubin
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A unified approach to algebraic set theory [PDF]
, 2007 Introduction . This short paper provides a summary of the tutorial on categorical logic given by the second named author at the Logic Colloquium in Nijmegen.
B. V. D. Berg, I. Moerdijk
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Constructive Set Theory and Brouwerian Principles
Journal of universal computer science (Online), 2005 The paper furnishes realizability models of constructive Zermelo-Fraenkel set theory, CZF, which also validate Brouwerian principles such as the axiom of continuous choice (CC), the fan theorem (FT), and monotone bar induction (BIM), and thereby ...
M. Rathjen
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On Interpretations of Arithmetic and Set Theory
Notre Dame J. Formal Log., 2007 R. Kaye, Tin Lok Wong
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Internal Categoricity in Arithmetic and Set Theory
Notre Dame J. Formal Log., 2015 J. Väänänen, Tong Wang
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