Results 11 to 20 of about 37,312 (297)
Logics and admissible rules of constructive set theories [PDF]
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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VERY LARGE SET AXIOMS OVER CONSTRUCTIVE SET THEORIES [PDF]
The Bulletin of Symbolic Logic, 2022 Abstract We investigate large set axioms defined in terms of elementary embeddings over constructive set theories, focusing on $\mathsf {IKP}$ and $\mathsf {CZF}$ . Most previously studied large set axioms, notably, the constructive analogues of large cardinals below $0^\sharp
HANUL JEON, RICHARD MATTHEWS
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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 ...
EMMENEGGER, JACOPO, PALMGREN, ERIK
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Constructive Set Theory and Brouwerian Principles [PDF]
, 2005 JUCS - Journal of Universal Computer Science Volume Nr.
Michael Rathjen
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Formalizing Abstract Algebra in Constructive Set Theory
, 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. Then we can tell whether a given set with a binary operation is a group or not, and derive all properties ...
Yu, Xin, Hickey, Jason
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Direct spectra of Bishop spaces and their limits [PDF]
Logical Methods in Computer Science, 2021 We apply fundamental notions of Bishop set theory (BST), an informal theory that complements Bishop's theory of sets, to the theory of Bishop spaces, a function-theoretic approach to constructive topology.
Iosif Petrakis
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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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Al-Lisaniyyat, 2022 The aim of our paper is to present the Constructive Type Theory (CTT) and some related concepts for the Swedish logician Per Martin Löf, who constructed a formal logic system in order to establish a philosophical foundation of constructive mathematics ...
Terkia Mechouet, Farid Zidani
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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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Quotients, inductive types, and quotient inductive types [PDF]
Logical Methods in Computer Science, 2022 This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly infinitary operators ...
Marcelo P. Fiore +2 more
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