Results 11 to 20 of about 695,402 (315)
The generalised type-theoretic interpretation of constructive set theory [PDF]
, 2006 We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation.
Nicola Gambino, Peter Aczel
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Assembling the Proofs of Ordered Model Transformations [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on its parent ...
Maribel Fernández, Jeffrey Terrell
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VERY LARGE SET AXIOMS OVER CONSTRUCTIVE SET THEORIES [PDF]
The Bulletin of Symbolic LogicAbstract 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, R. G. Matthews
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Synthetic Dimensions in Constructive Set Theory
This paper explores the novel concept of "synthetic dimensions" within the framework of constructive set theory. While synthetic dimensions have gained prominence in physics, particularly in condensed matter systems where additional spatial or internal degrees of freedom are engineered, their rigorous and foundational treatment within constructive ...
SÉRGIO DE ANDRADE, PAULO
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A cumulative hierarchy of sets for constructive set theory [PDF]
Mathematical Logic Quarterly, 2014 The von Neumann hierarchy of sets is heavily used as a basic tool in classical set theory, being an underlying ingredient in many proofs and concepts. In constructive set theories like without the powerset axiom however, it loses much of its potency by ceasing to be a hierarchy of sets as its single stages become only classes. This article proposes an
Albert Ziegler
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Constructive mathematics - its set theory and practice
, 1974 The thesis falls naturally into two parts, in the first of which (comprising Chapter 1) there is laid down a set-theoretic foundation for constructive mathematics as understood by Errett Bishop and his followers. The work of this part closely follows the lines of the corresponding classical development of set theory by Anthony Morse, highlights several
Douglas Bridges
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Quotient topologies in constructive set theory and type theory
Annals of Pure and Applied Logic, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hajime Ishihara, Erik Palmgren
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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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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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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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