Recursion Theory : : Computational Aspects of Definability / / Chi Tat Chong, Liang Yu.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2015 Part 1
• VerfasserIn: Chong, Chi Tat,; Yu, Liang,
• 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
• Physical Description: 1 online resource (306 p.)

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.

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