Results 1 to 10 of about 695,402 (315)
Constructive Set Theory and Brouwerian Principles [PDF]
, 2020 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 ...
Michael Rathjen
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Formalizing Abstract Algebra in Constructive Set Theory [PDF]
, 2003 We present a machine-checked formalization of elementary abstract algebra in constructive set theory. Our formalization uses an approach where we start by specifying the group axioms as a collection of inference rules, defining a logic for groups.
Xin Yu, Hickey, Jason
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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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A Normalizing Intuitionistic Set Theory with Inaccessible Sets [PDF]
Logical Methods in Computer Science, 2007 We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs.
Wojciech Moczydlowski
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EXACT COMPLETION AND CONSTRUCTIVE THEORIES OF SETS [PDF]
The Journal of Symbolic Logic, 2020 AbstractIn the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Löf type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e., objects satisfying the axiom of choice ...
Jacopo Emmenegger, Erik Palmgren
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Logics and admissible rules of constructive set theories
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We finally provide examples of a number of set theories that are extensible.
Rosalie Iemhoff, Robert Paßmann
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A Note on OTM-Realizability and Constructive Set Theories [PDF]
, 2019 We define an ordinalized version of Kleene's realizability interpretation of intuitionistic logic by replacing Turing machines with Koepke's ordinal Turing machines (OTMs), thus obtaining a notion of realizability applying to arbitrary statements in the ...
Merlin Carl
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A characterization of trees with equal 2-domination and 2-independence numbers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$.
Christoph Brause +2 more
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Families of Sets in Constructive Measure Theory [PDF]
, 2022 We present the first steps of a predicative reconstruction of the constructive Bishop-Cheng measure theory. Working in a semi-formal elaboration of Bishop's set theory and invoking the notion of a set-indexed family of subsets (of a given set), we arrive at notions of a pre-integration space and of a pre-measure space.
Max Zeuner
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Normalization of IZF with Replacement [PDF]
Logical Methods in Computer Science, 2008 ZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call \izfr, along with its intensional counterpart \iizfr.
Wojciech Moczydlowski
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