Recursion Theory : : Computational Aspects of Definability / / Chi Tat Chong, Liang Yu.
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 f...
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| Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2015 Part 1 |
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| Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2015] ©2015 |
| Year of Publication: | 2015 |
| Language: | English |
| Series: | De Gruyter Series in Logic and Its Applications ,
8 |
| Online Access: | |
| Physical Description: | 1 online resource (306 p.) |
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Table of Contents:
- Frontmatter
- Preface
- Contents
- Part I: Fundamental theory
- 1 An introduction to higher recursion theory
- 2 Hyperarithmetic theory
- 3 Admissibility and constructibility
- 4 The theory of Π11-sets
- 5 Recursion-theoretic forcing
- 6 Set theory
- Part II: The story of Turing degrees
- 7 Classification of jump operators
- 8 The construction of Π11-sets
- 9 Independence results in recursion theory
- Part III: Hyperarithmetic degrees and perfect set property
- 10 Rigidity and biinterpretability of hyperdegrees
- 11 Basis theorems
- Part IV: Higher randomness theory
- 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