Classical recursion theory: the theory of functions and sets of natural numbers
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1989-1999
|
| Series: | Studies in logic and the foundations of mathematics
v. 125, 143 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Vol. 2 lacks other title information. - "First edition 1999"--V. 2, t.p. verso. - Vol. 2 published: Amsterdam ; New York : Elsevier Volume II of <IT>Classical Recursion Theory</IT> describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side Includes bibliographical references and indexes |
| Physical Description: | 1 Online-Ressource (2 v.) |
| ISBN: | 9780444502056 044450205X 0444872957 9780444872951 |
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| 500 | |a Volume II of <IT>Classical Recursion Theory</IT> describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side | ||
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Record in the Search Index
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| author | Odifreddi, Piergiorgio |
| author_facet | Odifreddi, Piergiorgio |
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| author_sort | Odifreddi, Piergiorgio |
| author_variant | p o po |
| building | Verbundindex |
| bvnumber | BV042317323 |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444502056 044450205X 0444872957 9780444872951 |
| language | English |
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| physical | 1 Online-Ressource (2 v.) |
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| publishDate | 1989 |
| publishDateSearch | 1989 |
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| publisher | North-Holland |
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| series2 | Studies in logic and the foundations of mathematics |
| spelling | Odifreddi, Piergiorgio Verfasser aut Classical recursion theory the theory of functions and sets of natural numbers Piergiorgio Odifreddi Amsterdam North-Holland 1989-1999 1 Online-Ressource (2 v.) txt rdacontent c rdamedia cr rdacarrier Studies in logic and the foundations of mathematics v. 125, 143 Vol. 2 lacks other title information. - "First edition 1999"--V. 2, t.p. verso. - Vol. 2 published: Amsterdam ; New York : Elsevier Volume II of <IT>Classical Recursion Theory</IT> describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side Includes bibliographical references and indexes Récursivité, Théorie de la Récursivité, Théorie de la ram Recursion theory fast Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd rswk-swf Rekursionstheorie (DE-588)4122329-9 s 1\p DE-604 http://www.sciencedirect.com/science/book/9780444502056 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Odifreddi, Piergiorgio Classical recursion theory the theory of functions and sets of natural numbers Récursivité, Théorie de la Récursivité, Théorie de la ram Recursion theory fast Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd |
| subject_GND | (DE-588)4122329-9 |
| title | Classical recursion theory the theory of functions and sets of natural numbers |
| title_auth | Classical recursion theory the theory of functions and sets of natural numbers |
| title_exact_search | Classical recursion theory the theory of functions and sets of natural numbers |
| title_full | Classical recursion theory the theory of functions and sets of natural numbers Piergiorgio Odifreddi |
| title_fullStr | Classical recursion theory the theory of functions and sets of natural numbers Piergiorgio Odifreddi |
| title_full_unstemmed | Classical recursion theory the theory of functions and sets of natural numbers Piergiorgio Odifreddi |
| title_short | Classical recursion theory |
| title_sort | classical recursion theory the theory of functions and sets of natural numbers |
| title_sub | the theory of functions and sets of natural numbers |
| topic | Récursivité, Théorie de la Récursivité, Théorie de la ram Recursion theory fast Recursion theory Rekursionstheorie (DE-588)4122329-9 gnd |
| topic_facet | Récursivité, Théorie de la Recursion theory Rekursionstheorie |
| url | http://www.sciencedirect.com/science/book/9780444502056 |
| work_keys_str_mv | AT odifreddipiergiorgio classicalrecursiontheorythetheoryoffunctionsandsetsofnaturalnumbers |