Higher Recursion Theory

This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.

Gerald E. Sacks (Author)

9781107168435, Cambridge University Press

Hardback, published 2 March 2017

360 pages
24 x 16.3 x 2.7 cm, 0.73 kg

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Perspectives in Logic series, is an almost self-contained introduction to higher recursion theory, in which the reader is only assumed to know the basics of classical recursion theory. The book is divided into four parts: hyperarithmetic sets, metarecursion, ?-recursion, and E-recursion. This text is essential reading for all researchers in the field.

Part I. Hyperarithmetic Sets: 1. Constructive ordinals and prod_1^1 sets
2. The hyperarithmetic hierarchy
3. Sigma_1^1 predicates of reals
4. Measure and forcing
Part II. Metarecursion: 5. Metarecursive enumerability
6. Hyperregularity and priority
Part III. ?-Recursion: 7. Admissibility and regularity
8. Priority arguments
9. Splitting, density and beyond
Part IV. E-Recursion: 10. E-closed structures
11. Forcing computations to converge
12. Selection and k-sections
13. E-recursively enumerable degrees
Bibliography
Subject index.

Subject Areas: Mathematical theory of computation [UYA], Number theory [PBH], Set theory [PBCH], Mathematical logic [PBCD]