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200106 ||| eng |
| 020 |
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|a 9781139031905
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| 050 |
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4 |
|a QA9.54
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| 100 |
1 |
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|a Schwichtenberg, Helmut
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| 245 |
0 |
0 |
|a Proofs and computations
|c Helmut Schwichtenberg, Stanley S. Wainer
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| 246 |
3 |
1 |
|a Proofs & Computations
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 2012
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| 300 |
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|a xiii, 465 pages
|b digital
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| 653 |
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|a Computable functions
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| 653 |
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|a Proof theory
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| 700 |
1 |
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|a Wainer, S. S.
|e [author]
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| 710 |
2 |
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|a Association for Symbolic Logic
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 490 |
0 |
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|a Perspectives in logic
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| 856 |
4 |
0 |
|u https://doi.org/10.1017/CBO9781139031905
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 511.352
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| 520 |
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|a Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic
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