Varieties of Constructive MathematicsCambridge University Press, 24. apr. 1987 - 149 strani 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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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 |
146 | |
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