ENGLISH

Higher Recursion Theory

By Gerald E. Sacks

Book information

Publisher
Springer
Year
1990
ISBN
3540193057, 9783540193050, 0387193057
LCC
QA9.6 .S23 1990
Language
english
Format
DJVU
Filesize
2 MB (2455898 bytes)
Series
Perspectives in mathematical logic
Pages
489\364
Topic
Mathematics Logic
Library
Kolxo3
DPI
600
Scanned
no
Time added
2009-12-04 00:34:26

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.

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