Higher Recursion Theory

Sacks, Gerald

ISBN 10: 3540193057 / ISBN 13: 9783540193050

Editore: Springer, Berlin, Germany, 1990

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0 Sewn binding. Cloth over boards. 359 p. Springer Series on Wave Phenomena. Audience: General/trade. Very good. Signed by previous owner. light shelf wear.

Codice articolo Alibris.0070382

Dati bibliografici

• Titolo: Higher Recursion Theory
• Editore: Springer, Berlin, Germany
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 3540193057
• ISBN 13: 9783540193050
• Rilegatura: Rilegato

Descrizione articolo

Riassunto

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.

Contenuti

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.