Recursion theory :: computational aspects of definability /
This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
Walter de Gruyter GmbH & Co., KG,
[2015]
|
| Schriftenreihe: | De Gruyter series in logic and its applications ;
8. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness. |
| Beschreibung: | 1 online resource (xiii, 306 pages) |
| Bibliographie: | Includes bibliographical reference (pages 295-301) and index. |
| ISBN: | 9783110275643 3110275643 9783110275650 3110275651 |
Internformat
MARC
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| 245 | 1 | 0 | |a Recursion theory : |b computational aspects of definability / |c Chi Tat Chong, Liang Yu. |
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| 588 | 0 | |a Print version record. | |
| 520 | |a This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Recursion theory. |0 http://id.loc.gov/authorities/subjects/sh85112012 | |
| 650 | 4 | |a Logic and Set Theory. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Mathematik. | |
| 650 | 4 | |a Recursion theory. | |
| 650 | 6 | |a Théorie de la récursivité. | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Recursion theory |2 fast | |
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| 880 | 0 | 0 | |6 505-00/(S |t Frontmatter -- |t Preface -- |t Contents -- |t 1 An introduction to higher recursion theory -- |t 2 Hyperarithmetic theory -- |t 3 Admissibility and constructibility -- |t 4 The theory of Π -- |t 5 Recursion-theoretic forcing -- |t 6 Set theory -- |t 7 Classification of jump operators -- |t 8 The construction of Π -- |t 9 Independence results in recursion theory -- |t 10 Rigidity and biinterpretability of hyperdegrees -- |t 11 Basis theorems -- |t 12 Review of classical algorithmic randomness -- |t 13 More on hyperarithmetic theory -- |t 14 The theory of higher randomness -- |t A Open problems -- |t B An interview with Gerald E. Sacks -- |t C Notations and symbols -- |t Bibliography -- |t Index -- |t Backmatter. |
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| author | Chong, C.-T. (Chi-Tat), 1949- Yu, Liang (Professor of mathematics) |
| author_GND | http://id.loc.gov/authorities/names/n83161355 http://id.loc.gov/authorities/names/n2015014185 |
| author_facet | Chong, C.-T. (Chi-Tat), 1949- Yu, Liang (Professor of mathematics) |
| author_role | aut aut |
| author_sort | Chong, C.-T. 1949- |
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| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.6 .C46 2015 |
| callnumber-search | QA9.6 .C46 2015 |
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| collection | ZDB-4-EBA |
| contents | Part I: Fundamental theory -- Part II: The story of turing degrees -- Part III: Hyperarithmetic degrees and perfect set properly -- Part IV: Higher randomness theory. |
| ctrlnum | (OCoLC)919338525 |
| dewey-full | 511.3/5 |
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| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/5 |
| dewey-search | 511.3/5 |
| dewey-sort | 3511.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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"><subfield code="a">This monograph presents recursion theory from a generalized and largely global point of view. 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| id | ZDB-4-EBA-ocn919338525 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:46Z |
| institution | BVB |
| isbn | 9783110275643 3110275643 9783110275650 3110275651 |
| language | English |
| oclc_num | 919338525 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 306 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Walter de Gruyter GmbH & Co., KG, |
| record_format | marc |
| series | De Gruyter series in logic and its applications ; |
| series2 | De Gruyter series in logic and its applications ; |
| spelling | Chong, C.-T. (Chi-Tat), 1949- author. https://id.oclc.org/worldcat/entity/E39PBJt8m4PHhJYfHR4DGBDpfq http://id.loc.gov/authorities/names/n83161355 Recursion theory : computational aspects of definability / Chi Tat Chong, Liang Yu. Berlin ; Boston : Walter de Gruyter GmbH & Co., KG, [2015] ©2015 1 online resource (xiii, 306 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter series in logic and its applications ; Volume 8 Includes bibliographical reference (pages 295-301) and index. Part I: Fundamental theory -- Part II: The story of turing degrees -- Part III: Hyperarithmetic degrees and perfect set properly -- Part IV: Higher randomness theory. Print version record. This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness. In English. Recursion theory. http://id.loc.gov/authorities/subjects/sh85112012 Logic and Set Theory. Mathematics. Mathematik. Recursion theory. Théorie de la récursivité. MATHEMATICS General. bisacsh Recursion theory fast Yu, Liang (Professor of mathematics), author. https://id.oclc.org/worldcat/entity/E39PCjBg4FgT7j7m9Jjdr78jqP http://id.loc.gov/authorities/names/n2015014185 has work: Recursion theory (Text) https://id.oclc.org/worldcat/entity/E39PCFPG3kmPXQXWDpVyyK7Hvd https://id.oclc.org/worldcat/ontology/hasWork Print version: Chong, C.-T. (Chi-Tat), 1949- Recursion theory. Berlin ; Boston : Walter de Gruyter GmbH & Co., KG, [2015] 9783110275551 (DLC) 2015008883 (OCoLC)904420459 De Gruyter series in logic and its applications ; 8. http://id.loc.gov/authorities/names/n99027177 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1050258 Volltext 505-00/(S Frontmatter -- Preface -- Contents -- 1 An introduction to higher recursion theory -- 2 Hyperarithmetic theory -- 3 Admissibility and constructibility -- 4 The theory of Π -- 5 Recursion-theoretic forcing -- 6 Set theory -- 7 Classification of jump operators -- 8 The construction of Π -- 9 Independence results in recursion theory -- 10 Rigidity and biinterpretability of hyperdegrees -- 11 Basis theorems -- 12 Review of classical algorithmic randomness -- 13 More on hyperarithmetic theory -- 14 The theory of higher randomness -- A Open problems -- B An interview with Gerald E. Sacks -- C Notations and symbols -- Bibliography -- Index -- Backmatter. |
| spellingShingle | Chong, C.-T. (Chi-Tat), 1949- Yu, Liang (Professor of mathematics) Recursion theory : computational aspects of definability / De Gruyter series in logic and its applications ; Part I: Fundamental theory -- Part II: The story of turing degrees -- Part III: Hyperarithmetic degrees and perfect set properly -- Part IV: Higher randomness theory. Recursion theory. http://id.loc.gov/authorities/subjects/sh85112012 Logic and Set Theory. Mathematics. Mathematik. Recursion theory. Théorie de la récursivité. MATHEMATICS General. bisacsh Recursion theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85112012 |
| title | Recursion theory : computational aspects of definability / |
| title_auth | Recursion theory : computational aspects of definability / |
| title_exact_search | Recursion theory : computational aspects of definability / |
| title_full | Recursion theory : computational aspects of definability / Chi Tat Chong, Liang Yu. |
| title_fullStr | Recursion theory : computational aspects of definability / Chi Tat Chong, Liang Yu. |
| title_full_unstemmed | Recursion theory : computational aspects of definability / Chi Tat Chong, Liang Yu. |
| title_short | Recursion theory : |
| title_sort | recursion theory computational aspects of definability |
| title_sub | computational aspects of definability / |
| topic | Recursion theory. http://id.loc.gov/authorities/subjects/sh85112012 Logic and Set Theory. Mathematics. Mathematik. Recursion theory. Théorie de la récursivité. MATHEMATICS General. bisacsh Recursion theory fast |
| topic_facet | Recursion theory. Logic and Set Theory. Mathematics. Mathematik. Théorie de la récursivité. MATHEMATICS General. Recursion theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1050258 |
| work_keys_str_mv | AT chongct recursiontheorycomputationalaspectsofdefinability AT yuliang recursiontheorycomputationalaspectsofdefinability |