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A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice [PDF]
Logical Methods in Computer Science, 2021 We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's thesis and axiom of choice.
Maria Emilia Maietti +2 more
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ریاضی و جامعه, 2022 In this article, we have a brief historical overview of the facts around the axiom of choice (AC) in set theory. In this regard, we will state some of the most important equivalents of AC and also some of the weaker forms of AC.
سید محمد امین خاتمی
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A program for the full axiom of choice [PDF]
Logical Methods in Computer Science, 2021 The theory of classical realizability is a framework for the Curry-Howard correspondence which enables to associate a program with each proof in Zermelo-Fraenkel set theory.
Jean-Louis Krivine
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Mathematics, 2022 I begin the study of a hierarchy of (hereditarily)
Gunter Fuchs
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Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice [PDF]
Logical Methods in Computer Science, 2022 In this work we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions sufficient to generate Sambin's Positive topologies, namely Martin-L\"of ...
Maria Emilia Maietti +2 more
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Relative Symmetric Reductions under Multi-Choice Non-Transferable-Utility Situations
Mathematics, 2022 In many game-theoretical results, the reduction axiom and its converse have been regarded as important requirements under axiomatic processes for solutions.
Yu-Hsien Liao
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Quantum Theory without the Axiom of Choice, and Lefschetz Quantum Physics
Physics, 2023 In this paper, we discuss quantum formalisms that do not use the axiom of choice. We also consider the fundamental problem that addresses the (in)correctness of having the complex numbers as the base field for Hilbert spaces in the København ...
Koen Thas
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The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
Bulletin of the Section of Logic, 2023 In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC).
Tin Adlešić, Vedran Čačić
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Axiom of Choice and Complementation [PDF]
Proceedings of the American Mathematical Society, 1975 It is shown that an intuitionistic model of set theory with the axiom of choice has to be a classical one.
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On the Nielsen-Schreier Theorem in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2022 We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types.
Andrew W Swan
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