Recursion theory : computational aspects of definability / Chi Tat Chong, Liang Yu.

Format:

Book

Author/Creator:

Chong, C.-T. (Chi-Tat), 1949- author.

Yu, Liang, author.

Series:

De Gruyter series in logic and its applications ; Volume 8.

De Gruyter Series in Logic and Its Applications, 1438-1893 ; Volume 8

Language:

English

Subjects (All):

Recursion theory.

Physical Description:

1 online resource (322 p.)

Edition:

1st ed.

Place of Publication:

Berlin, [Germany] ; Boston, [Massachusetts] : De Gruyter, 2015.

Language Note:

English

Summary:

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.

Contents:

Front matter

Preface

Contents

Part I: Fundamental theory

1 An introduction to higher recursion theory

2 Hyperarithmetic theory

3 Admissibility and constructibility

4 The theory of Π1 1-sets

5 Recursion-theoretic forcing

6 Set theory

Part II: The story of Turing degrees

7 Classification of jump operators

8 The construction of Π1 1-sets

9 Independence results in recursion theory

Part III: Hyperarithmetic degrees and perfect set property

10 Rigidity and bi-interpretability 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9783110381290

311038129X

9783110275643

3110275643

OCLC:

919182882