Results 11 to 20 of about 3,715 (167)
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
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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.
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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
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Properties of Finitely Supported Self - Mappings on the Finite Powerset of Atoms [PDF]
Computer Science Journal of Moldova, 2021 The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every classical structure is replaced by a finitely supported structure according to the action of a group of permutations of ...
Andrei Alexandru
doaj
Mathematics, 2022 The theory of finitely supported structures is used for dealing with very large sets having a certain degree of symmetry. This framework generalizes the classical set theory of Zermelo-Fraenkel by allowing infinitely many basic elements with no internal ...
Andrei Alexandru, Gabriel Ciobanu
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Carnap's philosophy of mathematics
Philosophy Compass, Volume 17, Issue 11, November 2022., 2022 Abstract For several decades, Carnap's philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture.
Benjamin Marschall
wiley +1 more source
Mechanism Design With Limited Commitment
Econometrica, Volume 90, Issue 4, Page 1463-1500, July 2022., 2022 We develop a tool akin to the revelation principle for dynamic mechanism‐selection games in which the designer can only commit to short‐term mechanisms. We identify a canonical class of mechanisms rich enough to replicate the outcomes of any equilibrium in a mechanism‐selection game between an uninformed designer and a privately informed agent.
Laura Doval, Vasiliki Skreta
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Towards a constructive simplicial model of Univalent Foundations
Journal of the London Mathematical Society, Volume 105, Issue 2, Page 1073-1109, March 2022., 2022 Abstract We provide a partial solution to the problem of defining a constructive version of Voevodsky's simplicial model of Univalent Foundations. For this, we prove constructive counterparts of the necessary results of simplicial homotopy theory, building on the constructive version of the Kan‐Quillen model structure established by the second‐named ...
Nicola Gambino, Simon Henry
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Solutions of Extension and Limits of Some Cantorian Paradoxes
Mathematics, 2020 Cantor thought of the principles of set theory or intuitive principles as universal forms that can apply to any actual or possible totality. This is something, however, which need not be accepted if there are totalities which have a fundamental ...
Josué-Antonio Nescolarde-Selva +4 more
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