Varieties of Constructive Mathematics

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Cambridge University Press, 24. apr. 1987 - 149 strani
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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.
 

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Vsebina

Foundations of Constructive Mathematics
1
Basic constructions
6
Informal intuitionistic logic
10
Choice axioms
11
Real numbers
12
Problems
14
Notes
16
2 Constructive Analysis
18
3 Splitting fields
79
4 Uniqueness of splitting fields
82
5 Finitely presented modules
87
6 Noetherian rings
91
Problems
97
Notes
99
5 Intuitionism
103
2 Continuous choice
106

2 Baires theorem revisited
21
3 Located subsets
26
4 Totally Bounded Spaces
28
5 Bounded Linear Maps
34
6 Compactly Generated Banach Spaces
41
Problems
44
Notes
47
1 Progranming Systems and Omniscience Principles
49
2 Continuity and intermediate values
54
3 Speckers Sequence
58
4 The HeineBorel Theorem
60
5 Moduli of continuity and cozero sets
64
6 Ceitins theorem
67
Problems
71
Notes
73
1 General considerations
75
2 Factoring
76
3 Uniform continuity
110
4 The creating subject and Markovs principle
116
Problems
117
Notes
119
1 The Three Varieties
120
2 Positivevalued Continuous Functions
122
Problems
129
Notes
130
1 Intuitionistic propositional calculus
131
2 Predicate calculus
134
3 The sheaf model CX
138
4 Presheaf topos models
141
Problems
143
Notes
144
INDEX
146
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Varieties of Constructive Mathematics
Douglas Bridges,Fred Richman,Bridges/Richman
Predogled ni na voljo - 1987

Pogosti izrazi in povedi

algebra analysis arbitrary assertion assume axiom Banach space binary sequence BISH Brouwer Brouwerian called Chapter choice choose classical closed coherent compact complete condition consider constructive mathematics containing continuous map converges Corollary countable counterexamples defined definition dense detachable subset discrete field elements enumeration equal equivalent example exists extend factor false field finite-dimensional finitely follows formula given groups Hence holds induction interpretation interval intuitionistic intuitionistic logic Lemma LLPO located logic Markov's principle metric space Noetherian nonempty nonvoid nonzero normed linear space Note notion object partial function pointwise continuous polynomial positive integer presented problem Proof Proposition prove rational numbers real number recursive relation restriction result ring RUSS satisfies separable sequence statement subset Suppose theorem theory topos totally bounded true uniform uniformly continuous whence

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NaslovVarieties of Constructive Mathematics
Količina 97 od Lecture note series, London Mathematical Society, ISSN 0076-0552
97. izdaja od London Mathematical Society Lecture Note Series, London Mathematical Society, ISSN 0076-0552
Količina 97 od London Mathematical Society: London Mathematical Society lecture note series
AvtorjiDouglas Bridges, Fred Richman, Bridges/Richman
Avtorji prispevkovJ. W. S. Cassels, N. J. Hitchin
Izdajailustrirana, ponatisnjena
ZaložnikCambridge University Press, 1987
ISBN0521318025, 9780521318020
Dolžina149 strani
  
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