Higher Recursion Theory (Perspectives in Mathematical Logic)

Sacks, Gerald E.

ISBN 10: 3540193057 / ISBN 13: 9783540193050

Published by Springer, 1990

Very GoodDust Jacket may NOT BE INCLUDED.CDs may be missing. Seller Inventory # ERICA83735401930573

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.

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

Bibliographic Details

Title: Higher Recursion Theory (Perspectives in ...
Publisher: Springer
Publication Date: 1990
Binding: Hardcover
Condition: Very Good
Dust Jacket Condition: Dust Jacket Included
Book Type: book