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Varieties of Constructive Mathematics : London Mathematical Society Lecture Notes - Douglas S. Bridges

Varieties of Constructive Mathematics

London Mathematical Society Lecture Notes

Paperback Published: 6th July 1987
ISBN: 9780521318020
Number Of Pages: 160

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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.

The Foundations of Contructive Mathematics
Existence and omnisciencep. 1
Basic constructionsp. 6
Informal intuitionistic logicp. 11
Choice axiomsp. 11
Real numbersp. 12
Problemsp. 14
Notesp. 16
Constructive Analysis
Complete metric spacesp. 18
Baire's theorem revisitedp. 21
Located subsetsp. 26
Totally bounded spacesp. 28
Bounded linear mapsp. 34
Compactly generated Banach spacesp. 41
Problemsp. 44
Notesp. 47
Russian Constructive Mathematics
Programming systems and omniscience principlesp. 49
Continuity and intermediate valuesp. 54
Specker's sequencep. 58
The Heine-Borel theoremp. 60
Moduli of continuity and cozero setsp. 64
Ceitin's theoremp. 67
Problemsp. 71
Notesp. 73
Constructive Algebra
General considerationsp. 75
Factoringp. 76
Splitting fieldsp. 79
Uniqueness of splitting fieldsp. 82
Finitely presented modulesp. 87
Noetherian ringsp. 91
Problemsp. 97
Notesp. 99
Intuitionism
Sequence spacesp. 103
Continuous choicep. 106
Uniform continuityp. 110
The creating subject and Markov's principlep. 116
Problemsp. 117
Notesp. 119
Contrasting Varieties
The three varietiesp. 120
Positive-valued continuous functionsp. 122
Problemsp. 129
Notesp. 130
Intuitionistic Logic and Topos Theory
Intuitionistic propositional calculusp. 131
Predicate calculusp. 134
The sheaf model C(X)p. 138
Presheaf topos modelsp. 140
Problemsp. 143
Notesp. 144
Indexp. 146
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521318020
ISBN-10: 0521318025
Series: London Mathematical Society Lecture Notes
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 160
Published: 6th July 1987
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 23.37 x 15.44  x 1.19
Weight (kg): 0.26

Earn 134 Qantas Points
on this Book