| Proofs and Computations Contributor(s): Schwichtenberg, Helmut (Author), Wainer, Stanley S. (Author) |
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ISBN: 1139031902 ISBN-13: 9781139031905 Publisher: Cambridge University Press OUR PRICE: $140.25 Product Type: Open Ebook - Other Formats Published: January 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Logic |
| Dewey: 511.352 |
| Series: Perspectives in Logic |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 G del'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. |
Contributor Bio(s): Wainer, Stanley S.: - Stanley S. Wainer is an Emeritus Professor of Mathematics at the University of Leeds and a past-President of the British Logic Colloquium.Schwichtenberg, Helmut: - Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universitat Munchen. He has recently developed the 'proof-assistant' MINLOG, a computer-implemented logic system for proof/program development and extraction of computational content. |