This is an introduction to, and survey of, the constructive approaches to pure mathematics. The authors emphasise the viewpoint of Errett Bishop's school, but intuitionism. Russian constructivism and recursive analysis are also treated, with comparisons between the various approaches included where appropriate. Constructive mathematics is now enjoying a revival, with interest from not only logicans but also category theorists, recursive function theorists and theoretical computer scientists. This account for non-specialists in these and other disciplines.
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A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate. -- Book Description
Book Description
A survey of constructive approaches to pure mathematics emphasizing the viewpoint of Errett Bishop's school. Considers intuitionism, Russian constructivism, and recursive analysis, with comparisons among the various approaches included where appropriate.
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First Sentence:
We engage in constructive mathematics from a desire to clarify the meaning of mathematical terminology and practice - in particular, the meaning of existence in a mathematical context. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
detachable subset, finitely enumerable set, increasing binary sequence, detachable bar, standard classical proof, topos models, finite routine, cozero sets, totally bounded space, recursive algebra, metric complement, countable choice, omniscience principles, fan theorem, factorial field, uniformly continuous map, denial inequality, uniform continuity theorem, pointwise continuous, simplest axiom, recursive mathematics, generated left ideals, located subset, constructive mathematics, countable domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Theorem Let, Corollary Let, Symbolic Logic, Proposition Let, Prove Proposition New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We engage in constructive mathematics from a desire to clarify the meaning of mathematical terminology and practice - in particular, the meaning of existence in a mathematical context. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
detachable subset, finitely enumerable set, increasing binary sequence, detachable bar, standard classical proof, topos models, finite routine, cozero sets, totally bounded space, recursive algebra, metric complement, countable choice, omniscience principles, fan theorem, factorial field, uniformly continuous map, denial inequality, uniform continuity theorem, pointwise continuous, simplest axiom, recursive mathematics, generated left ideals, located subset, constructive mathematics, countable domain Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lemma Let, Theorem Let, Corollary Let, Symbolic Logic, Proposition Let, Prove Proposition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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26
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- Elements of Intuitionism (Oxford Logic Guides) by Michael Dummett in Front Matter
- Constructive Analysis (Grundlehren Der Mathematischen Wissenschaften) by Errett Bishop in Front Matter
- Coding the Universe (London Mathematical Society Lecture Note Series) by A. Beller in Front Matter
- Mathematical Statistics (Chapman & Hall/CRC Texts in Statistical Science) by Keith Knight in Front Matter
- Implementing Mathematics With the Nuprl Proof Development System by R. L. Constable in Front Matter
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- From Sets and Types to Topology and Analysis: Towards Practicable Foundations for Constructive Mathematics (Oxford Logic Guides) by Laura Crosilla on 4 pages
- Recursive Model Theory, Volume Volume 1 (Studies in Logic and the Foundations of Mathematics) by Author Unknown on page 521, and page 592
- Philosophy of Science, Logic and Mathematics in the 20th Century: Routledge History of Philosophy Volume 9 by Stuart G. Shanker on page 45, and page 117
- Computability : Computable Functions Logic and the Foundations of Math (Wadsworth&Brooks/Cole Mathematics Series) by Richard L. Epstein on page 269, and Back Matter
- Reuniting the Antipodes: Constructive and Nonstandard Views of the Continuum (Synthese Library) by Peter Schuster on page 36, and page 60
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