HIGHER RECURSION THEORY - PERSPECTIVES IN MATHEMATIC LOGIC - Couverture souple

Sacks, Gerald-E

Couverture souple

ISBN 10 : 3540193057 ISBN 13 : 9783540193050

Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1990

Synopsis

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.

A propos du livre

Présentation de l'éditeur

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.

Biographie de l'auteur

Gerald E. Sacks works in the Department of Mathematics at Harvard University, Massachusetts and at the Massachusetts Institute of Technology.

Détails de l'édition

• Éditeur: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Date d'édition: 1990
• ISBN 10: 3540193057
• ISBN 13: 9783540193050
• Reliure: Broché
• Langue: anglais
• Nombre de pages: 359
• Coordonnées du fabricant: non disponible