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Item Details
| Title:
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PROOFS AND COMPUTATIONS
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| By: |
Helmut Schwichtenberg, Stanley S. Wainer |
| Format: |
Hardback |
| List price:
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£75.00 |
| Our price: |
£65.63 |
| Discount: |
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| You save:
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£9.37 |
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| ISBN 10: |
0521517699 |
| ISBN 13: |
9780521517690 |
| Availability: |
Usually dispatched within 1-3 weeks.
 Delivery
rates
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| Stock: |
Currently 0 available |
| Publisher: |
CAMBRIDGE UNIVERSITY PRESS |
| Pub. date: |
15 December, 2011 |
| Series: |
Perspectives in Logic |
| Pages: |
480 |
| Description: |
This major graduate-level text provides a detailed, self-contained coverage of proof theory. |
| Synopsis: |
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 Godel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to PI11-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 PI11-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. |
| Illustrations: |
8 b/w illus. |
| Publication: |
UK |
| Imprint: |
Cambridge University Press |
| Returns: |
Returnable |
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