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Recursion Theory
Computational Aspects of Definability
Buch von Liang Yu (u. a.)
Sprache: Englisch

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Beschreibung
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. 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 techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory.
The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. 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 techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory.
The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Über den Autor
Chi Tat Chong, National University of Singapore; Liang Yu, Nanjing University, Jiangsu, China.
Inhaltsverzeichnis
Preliminaries

1. ¿11-uniformization and Applications to Turing Degrees

2. Rigidity of Hyperdegrees

3. Basis Theorems and ¿11-Hyperarithmetic

4. The Jump Operator

5. Independence Results in the Turing Degrees

6. Higher Randomness

References

Index

Details
Erscheinungsjahr: 2015
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 322
Reihe: ISSN
Inhalt: XIV
306 S.
ISBN-13: 9783110275551
ISBN-10: 3110275554
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Yu, Liang
Chong, Chi Tat
Hersteller: De Gruyter
ISSN
Maße: 246 x 175 x 23 mm
Von/Mit: Liang Yu (u. a.)
Erscheinungsdatum: 30.07.2015
Gewicht: 0,727 kg
preigu-id: 104462364
Über den Autor
Chi Tat Chong, National University of Singapore; Liang Yu, Nanjing University, Jiangsu, China.
Inhaltsverzeichnis
Preliminaries

1. ¿11-uniformization and Applications to Turing Degrees

2. Rigidity of Hyperdegrees

3. Basis Theorems and ¿11-Hyperarithmetic

4. The Jump Operator

5. Independence Results in the Turing Degrees

6. Higher Randomness

References

Index

Details
Erscheinungsjahr: 2015
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 322
Reihe: ISSN
Inhalt: XIV
306 S.
ISBN-13: 9783110275551
ISBN-10: 3110275554
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Yu, Liang
Chong, Chi Tat
Hersteller: De Gruyter
ISSN
Maße: 246 x 175 x 23 mm
Von/Mit: Liang Yu (u. a.)
Erscheinungsdatum: 30.07.2015
Gewicht: 0,727 kg
preigu-id: 104462364
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