Results 1 to 10 of about 109,181 (158)
Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice [PDF]
Logical Methods in Computer Science, 2022 In this work we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions sufficient to generate Sambin's Positive topologies, namely Martin-L\"of ...
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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Foundations of Mathematics and Mathematical Practice. The Case of Polish Mathematical School
Studia Historiae Scientiarum, 2022 The foundations of mathematics cover mathematical as well as philosophical problems. At the turn of the 20th century logicism, formalism and intuitionism, main foundational schools were developed.
Jan Woleński
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Computer Verified Exact Analysis (Tutorial) [PDF]
, 2009 This tutorial will illustrate how to use the Coq proof assistant to implement effective and provably correct computation for analysis. Coq provides a dependently typed functional programming language that allows users to specify both programs and formal ...
O\u27Connor, Russell +2 more
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A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice [PDF]
, 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.
Maietti, Maria Emilia +2 more
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Constructive Mathematics in Theory and Programming Practice [PDF]
, 1999 The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics(BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of ...
Bridges, Douglas, Reeves, Steve
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The Uses of Argument in Mathematics [PDF]
, 2005 Stephen Toulmin once observed that `it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate'. Might the application of Toulmin's layout of arguments to mathematics remedy this oversight?
Alexander George +13 more
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Constructive set theory and Brouwerian principles [PDF]
, 2005 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 ...
Rathjen, M
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Variations on the Theme of Conning in Mathematical Economics [PDF]
, 2007 The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic.
Velupillai, Kumaraswamy
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Quotient completion for the foundation of constructive mathematics [PDF]
, 2013 We apply some tools developed in categorical logic to give an abstract description of constructions used to formalize constructive mathematics in foundations based on intensional type theory.
Maietti, Maria Emilia +1 more
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