Classical Recursion Theory
Theory of Functions and Sets of Natural Numbers
Published in January 1989
Book
Paperback/Softback
686 pages
978-0-444-87295-1 (ISBN)
Description
1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Godel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 230 mm
ISBN-13
978-0-444-87295-1 (9780444872951)
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Schweitzer Classification
Other editions
Additional editions
E-Book
02/1992
Elsevier
€69.95
Available for download
Content
Recursiveness and Computability. Induction. Systems of Equations. Arithmetical Formal Systems. Turing Machines. Flowcharts. Functions as Rules. Arithmetization. Church's Thesis. Basic Recursion Theory. Partial Recursive Functions. Diagonalization. Partial Recursive Functionals. Effective Operations. Indices and Enumerations. Retraceable and Regressive Sets. Post's Problem and Strong Reducibilities. Post's Problem. Simple Sets and Many-One Degrees. Hypersimple Sets and Truth-Table Degrees. Hyperhypersimple Sets and Q-Degrees. A Solution to Post's Problem. Creative Sets and Completeness. Recursive Isomorphism Types. Variations of Truth-Table Reducibility. The World of Complete Sets. Formal Systems and R.E. Sets. Hierarchies and Weak Reducibilities. The Arithmetical Hierarchy. The Analytical Hierarchy. The Set-Theoretical Hierarchy. The Constructible Hierarchy. Turing Degrees. The Language of Degree Theory. The Finite Extension Method. Baire Category. The Coinfinite Extension Method. The Tree Method. Initial Segments. Global Properties. Degree Theory with Jump. Many-One and Other Degrees. Distributivity. Countable Initial Segments. Uncountable Initial Segments. Global Properties. Comparison of Degree Theories. Structure Inside Degrees. Bibliography. Index.