Gerald E. SacksCambridge University Press, 3/2/2017EAN 9781107168435, ISBN10: 1107168430Hardcover, 360 pages, 24 x 16.3 x 2.7 cmLanguage: EnglishSince 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 Sets1. Constructive ordinals and \prod_1^1 sets2. The hyperarithmetic hierarchy3. \Sigma_1^1 predicates of reals4. Measure and forcingPart II. Metarecursion5. Metarecursive enumerability6. Hyperregularity and priorityPart III. α-Recursion7. Admissibility and regularity8. Priority arguments9. Splitting, density and beyondPart IV. E-Recursion10. E-closed structures11. Forcing computations to converge12. Selection and k-sections13. E-recursively enumerable degreesBibliographySubject index.
