Higher Recursion Theory (Perspectives in Mathematical Logic)

Gerald E. Sacks

ISBN 10: 364205742X / ISBN 13: 9783642057427

Published by Springer, 2010

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Bibliographic Details

• Title: Higher Recursion Theory (Perspectives in Mathematical Logic)
• Publisher: Springer
• Publication Date: 2010
• Language: English
• ISBN 10: 364205742X
• ISBN 13: 9783642057427
• Binding: paperback
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

About this title

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.