Higher Recursion Theory [Hardcover]

This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.This introduction to higher recursion theory is essential reading for all researchers in the field. It is divided into four parts: hyperarithmetic sets, metarecursion, ?-recursion, and E-recursion.This introduction to higher recursion theory is essential reading for all researchers in the field. It is divided into four parts: hyperarithmetic sets, metarecursion, ?-recursion, and E-recursion.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.