UID:
almafu_9959234629002883
Umfang:
1 online resource (x, 149 pages) :
,
digital, PDF file(s).
ISBN:
1-139-88173-6
,
1-107-36624-0
,
1-107-37097-3
,
1-107-36133-8
,
1-107-36939-8
,
1-299-40404-9
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1-107-36378-0
,
0-511-56566-6
Serie:
London Mathematical Society lecture note series ; 97
Inhalt:
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.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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Cover; Title; Copyright; Preface; Contents; 1. Foundations of Constructive Mathematics; 1. Existence and omniscience; 2. Basic constructions; 3. Informal intuitionistic logic; 4. Choice axioms; 5. Seal numbers; Problems; Notes; 2. Constructive Analysis; 1. Complete metric spaces; 2. Baire's theorem revisited; 3. Located subsets; 4. Totally Bounded Spaces; 5. Bounded Linear Maps; 6. Compactly Generated Banach Spaces; Problems; Notes; 3. Russian Constructive Mathematics; 1. Programming Systems and Omniscience Principles; 2. Continuity and intermediate values; 3. Specker's Sequence
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4. The Helne-Borel Theorem5. Moduli of continuity and cozero sets; 6. Ceitin's theorem; Problems; Notes; 4. Constructive Algebra; 1. General considerations; 2. Factoring; 3. Splitting fields; 4. Uniqueness of splitting fields; 5. Finitely presented modules; 6. Noetherian rings; Problems; Notes; 5. Intuitionism; 1. Sequence spaces; 2. Continuous choice; 3. Uniform continuity; 4. The creating subject and Markov's principle; Problems; Notes; 6. Contrasting Varieties; 1. The Three Varieties; 2. Positive-valued Continuous Functions; Problems; Notes; 7. Intuitionistic Logic and Topos Theory
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1. Intuitionistic prepositional calculus2. Predicate calculus; 3. The sheaf model C(X); 4. Presheaf topos models; Problems; Notes; Index
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English
Weitere Ausg.:
ISBN 0-521-31802-5
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9780511565663
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