
Higher Recursion Theory
Gerald E. Sacks(Author)
Springer (Publisher)
Published on 8. December 2010
Book
Paperback/Softback
XV, 345 pages
978-3-642-05742-7 (ISBN)
Article exhausted; check different version
Description
Hyperarithmetic theory is the first step beyond classical recursion theory. It is the primary source of ideas and examples in higher recursion theory. It is also a crossroad for several areas of mathematical logic: in set theory it is an initial segment of Godel's L; in model theory, the least admissible set after; in descriptive set theory, the setting for effective arguments. In this book, hyperarithmetic theory is developed at length and used to lift classical recursion theory from integers to recursive ordinals (metarecursion). Two further liftings are then made, first ordinals ( -recursion) and then to sets (E-recursion). Techniques such as finite and infinite injury, forcing and fine structure and extended and combined Dynamic and syntactical methods are contrasted. Several notions of reducibility and computation are compared. Post's problem is answere affirmatively in all three settings. This long-awaited volume of the -series will be a "Must" for all working in the field.
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 1990
Language
English
Place of publication
Berlin
Germany
Target group
Professional and scholarly
Research
Product notice
Paperback (trade)
Illustrations
XV, 345 p.
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 19 mm
Weight
551 gr
ISBN-13
978-3-642-05742-7 (9783642057427)
DOI
10.1007/978-3-662-12013-2
Schweitzer Classification
Other editions
Additional editions

Gerald E. Sacks
Higher Recursion Theory
Book
10/1990
1st Edition
Springer
€85.59
Article exhausted; check different version
Content
Contents: Hyperarithmetic Sets: Constructive Ordinals and Sets. The Hyperarithmetic Hierarchy. Predicates of Reals. Measure and Forcing.- Metarecursion: Metarecursive Enumerability. Hyperregularity and Priority.- -Recursion: Admissibility and Regularity. Priority Arguments. Splitting, Density and Beyond.- E-Recursion: E-closed Structures.- Forcing Computations to Converge.- Selection and k-Sections.- E-Recursively Enumerable Degrees.- Bibliography.- Subject Index.