Classical Recursion Theory - 1st Edition - ISBN: 9780444894830, 9780080886596

Classical Recursion Theory, Volume 125

1st Edition

The Theory of Functions and Sets of Natural Numbers

Authors: P. Odifreddi
eBook ISBN: 9780080886596
Paperback ISBN: 9780444894830
Imprint: North Holland
Published Date: 4th February 1992
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Table of Contents

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.


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 Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation.


Details

Language:
English
Copyright:
© North Holland 1989
Published:
Imprint:
North Holland
eBook ISBN:
9780080886596
Paperback ISBN:
9780444894830

Reviews

@from:G.E. Sacks, Harvard University and M.I.T. @qu:Odifreddi has written a delightful yet scholarly treatise... @source: @from:C. Calude @qu:An impressive presentation of classical recursion theory... highly recommended to everyone interested in recursion theory. @source:Zentralblatt für Mathematik @qu:A must as a reference manual for any mathematician, philosopher or theoretical computer scientist who deals with issues of computability. @source:Mathematical Reviews @qu:An incredible wealth of information, including much that occurs for the first time in book form. @source:Journal of Symbolic Logic


About the Authors

P. Odifreddi Author

Affiliations and Expertise

University of Turin, Italy