Results 11 to 20 of about 496,419 (187)
A class of higher inductive types in Zermelo‐Fraenkel set theory [PDF]
Mathematical Logic Quarterly, Volume 68, Issue 1, Page 118-127, February 2022., 2022 Abstract We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo‐Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class includes the example of unordered trees of any arity.
Andrew Swan
wiley +4 more sources
Paraconsistent and Paracomplete Zermelo-Fraenkel Set Theory [PDF]
The Review of Symbolic Logic, 2022 We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false.
Yurii Khomskii, Hrafn Valtýr Oddsson
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The continuum hypothesis: Its independence from Zermelo-Fraenkel set theory and impact on mathematical foundations [PDF]
Theoretical and Natural Science, 2023 The Continuum Hypothesis, originally posited by the pioneering mathematician Georg Cantor in the latter part of the 19th century, stands as a cornerstone inquiry in the realm of set theory.
Yaming Zheng
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A positive function with vanishing Lebesgue integral in Zermelo-Fraenkel set theory [PDF]
, 2017 Can a positive function on R have zero Lebesgue integral? It depends on how much choice one has.
Vladimir Kanovei, Mikhail G. Katz
semanticscholar +4 more sources
Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience [PDF]
Annals of Pure and Applied Logic, 2013 Michael Rathjen
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A Nominalist Alternative to Reference by Abstraction. [PDF]
Theoria, 2023 Abstract In his recent book Thin Objects, Øystein Linnebo (2018) argues for the existence of a hierarchy of abstract objects, sufficient to model ZFC, via a novel and highly interesting argument that relies on a process called dynamic abstraction. This paper presents a way for a nominalist, someone opposed to the existence of abstract objects, to avoid
Pearce GR.
europepmc +2 more sources
CONTRADICTIONS WITHIN ZERMELO–FRAENKEL SET THEORY WITH AXIOM OF CHOICE
, 2020 By using a counterexample to the known equivalent of the axiom of choice (Krull’s theorem about maximal ideal existence) contradictions within Zermelo–Fraenkel set theory with axiom of choice was shown.
O. Kolos
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Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic, 2020 A major question asked during the development of ZF was what system of logic should be used as its framework. Logicians eventually agreed that the framework itself should not depend very much on set-theoretic reasoning.
Seymour Hayden
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When cardinals determine the power set: inner models and Härtig quantifier logic
Mathematical Logic Quarterly, Volume 69, Issue 4, Page 460-471, November 2023., 2023 Abstract We show that the predicate “x is the power set of y” is Σ1(Card)$\Sigma _1(\operatorname{Card})$‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here Card$\operatorname{Card}$ is a predicate true of just the infinite cardinals.
Jouko Väänänen, Philip D. Welch
wiley +1 more source
Thin Mereological Sums, Abstraction, and Interpretational Modalities
Theoria, Volume 89, Issue 3, Page 338-355, June 2023., 2023 Abstract Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non‐mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to ...
Giorgio Lando
wiley +1 more source