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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic Conference Proceedings eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
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| Series: | Perspectives in logic
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| Subjects: | |
| Links: | https://doi.org/10.1017/CBO9781139031905 https://doi.org/10.1017/CBO9781139031905 https://doi.org/10.1017/CBO9781139031905 https://doi.org/10.1017/CBO9781139031905 |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xiii, 465 pages) |
| ISBN: | 9781139031905 |
| DOI: | 10.1017/CBO9781139031905 |
Staff View
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| id | DE-604.BV043941783 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:49:17Z |
| institution | BVB |
| isbn | 9781139031905 |
| language | English |
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| publisher | Cambridge University Press |
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| series2 | Perspectives in logic |
| spelling | Schwichtenberg, Helmut 1942- Verfasser (DE-588)1023588242 aut Proofs and computations Helmut Schwichtenberg, Stanley S. Wainer Proofs & Computations Cambridge Cambridge University Press 2012 1 online resource (xiii, 465 pages) txt rdacontent c rdamedia cr rdacarrier Perspectives in logic Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Computable functions Proof theory Beweistheorie (DE-588)4145177-6 gnd rswk-swf Rekursionstheorie (DE-588)4122329-9 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s Rekursionstheorie (DE-588)4122329-9 s 1\p DE-604 Wainer, S. S. Sonstige oth Association for Symbolic Logic issuing body Sonstige oth Erscheint auch als Druckausgabe 978-0-521-51769-0 https://doi.org/10.1017/CBO9781139031905 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schwichtenberg, Helmut 1942- Proofs and computations Computable functions Proof theory Beweistheorie (DE-588)4145177-6 gnd Rekursionstheorie (DE-588)4122329-9 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4122329-9 |
| 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 |
| topic | Computable functions Proof theory Beweistheorie (DE-588)4145177-6 gnd Rekursionstheorie (DE-588)4122329-9 gnd |
| topic_facet | Computable functions Proof theory Beweistheorie Rekursionstheorie |
| url | https://doi.org/10.1017/CBO9781139031905 |
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