Higher Recursion Theory (Perspectives in Logic)
Cambridge University Press, 3/2/2017
EAN 9781107168435, ISBN10: 1107168430
Hardcover, 360 pages, 24 x 16.3 x 2.7 cm
Language: English
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, α-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. α-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.