Proofs and computations:
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. Pa...
Gespeichert in:
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2012
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| Schriftenreihe: | Perspectives in logic
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| Links: | https://doi.org/10.1017/CBO9781139031905 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xiii, 465 Seiten) |
| ISBN: | 9781139031905 |
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| spelling | Schwichtenberg, Helmut 1942- Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer Proofs & Computations Cambridge Cambridge University Press 2012 1 Online-Ressource (xiii, 465 Seiten) txt c cr Perspectives in logic 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. Wainer, S. S. Erscheint auch als Druck-Ausgabe 9780521517690 |
| spellingShingle | Schwichtenberg, Helmut 1942- Proofs and computations |
| title | Proofs and computations |
| title_alt | Proofs & Computations |
| title_auth | Proofs and computations |
| title_exact_search | Proofs and computations |
| title_full | Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer |
| title_fullStr | Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer |
| title_full_unstemmed | Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer |
| title_short | Proofs and computations |
| title_sort | proofs and computations |
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