Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers

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Overview
Editorial Reviews
Product Details
Table of Contents

Overview

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.

Editorial Reviews

From the Publisher

G.E. Sacks, Harvard University and M.I.T.
Odifreddi has written a delightful yet scholarly treatise...

C. Calude
An impressive presentation of classical recursion theory... highly recommended to everyone interested in recursion theory.
Zentralblatt für Mathematik
A must as a reference manual for any mathematician, philosopher or theoretical computer scientist who deals with issues of computability.
Mathematical Reviews
An incredible wealth of information, including much that occurs for the first time in book form.
Journal of Symbolic Logic

Product Details

ISBN-13: 9780444894830
Publisher: Elsevier Science
Publication date: 2/28/1992
Series: Studies in Logic and the Foundations of Mathematics Series
Edition description: REPRINT
Edition number: 2
Pages: 692
Product dimensions: 1.45 (w) x 6.14 (h) x 9.21 (d)

Chapter Headings only. Preface. Introduction. VII. Theories of recursive functions. Measures of complexity. Speed of computations. Complexity classes. Time and space measures. Inductive inference. VIII Hierarchies of recursive functions. Small time and space bounds. Deterministic polynomial time. Nondeterministic polynomial time. The polynomial time hierarchy. Polynomial space. Exponential time and space. Elementary functions. Primitive recursive functions. &egr;0-Recursive functions. IX. Recursively enumerable sets. Global properties of recursive sets. Local properties of R.E. sets. Global properties of R.E. sets. Complexity of R.E. sets. Inductive inference of R.E. sets. X. Recursively enumerable degress. The finite injury priority method. Effective Baire category. The infinite injury priority method. The priority method. Many-one degrees. Turing degrees. Comparison of degree theories. Structure inside degrees. Index sets. XI. Limit sets. Jump classes.1-Generic degrees. Structure theory. Minimal degrees. Global properties. Many-one degrees. XII. Arithmetical sets. Forcing in arithmetic. Applications of forcing. Turing degrees of arithmetical sets. XIII. Arithmetical degrees. The theory of arithmetical degrees. An analogue of R.E. sets. An analogue of Post's problem. An analogue of the jump classes. Comparison with R.E. degrees. Enumeration degrees. Enumeration degrees. The theory of enumeration degrees. Enumeration degrees below 0'e. A model of the Lambda calculus. Bibliography. Notation index. Subject index.

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Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers / Edition 2