| Description |
1 online resource (2 volumes) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Studies in logic and the foundations of mathematics ; v. 125, 143 |
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Studies in logic and the foundations of mathematics ; v. 125, 143.
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| Summary |
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. |
| Contents |
Preface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index. |
| Note |
Vol. 2 lacks other title information. |
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"First edition 1999"--V. 2, t.p. verso |
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Vol. 2 published: Amsterdam; New York : Elsevier. |
| Bibliography |
Includes bibliographical references and indexes. |
| Contents |
v. 1. (v.125) -- v. 2 (v.143). |
| Note |
Print version record. |
| Access |
Use copy Restrictions unspecified star MiAaHDL |
| Reproduction |
Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL |
| System Details |
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL |
| Processing Action |
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL |
| Subject |
Recursion theory.
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Théorie de la récursivité.
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Recursion theory
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Récursivité, Théorie de la.
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| Other Form: |
Print version: Odifreddi, Piergiorgio, 1950- Classical recursion theory. Amsterdam ; New York : North-Holland ; New York, N.Y., USA : Sole distributors for the USA and Canada, Elsevier Science Pub. Co., 1989-1999 0444872957 9780444872951 (DLC) 88033481 (OCoLC)18907888 |
| ISBN |
9780444502056 |
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044450205X |
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0444872957 (v. 1) |
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9780444872951 (v. 1) |
| Standard No. |
AU@ 000048130744 |
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CHNEW 001006538 |
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DEBBG BV036962314 |
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DEBBG BV042317323 |
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DEBSZ 482354976 |
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GBVCP 878886427 |
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NZ1 12433492 |
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NZ1 15192873 |
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