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.
- ISBN10 311038129X
- ISBN13 9783110381290
- Publish Date 17 August 2015 (first published 30 July 2015)
- Publish Status Active
- Out of Print 9 April 2021
- Publish Country DE
- Imprint De Gruyter
- Format eBook
- Pages 320
- Language English
- URL https://degruyter.com/isbn/9783110381290