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| CLASSICAL RECURSION THEORY
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 The Theory of Functions and Sets of Natural Numbers
To order this title, and for more information, click here
By
P. Odifreddi, University of Turin, Italy
Included in series
Studies in Logic and the Foundations of Mathematics, 125
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.
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.
Bibliographic & ordering Information
Paperback, publication date: FEB-1992
ISBN-13: 978-0-444-89483-0
ISBN-10: 0-444-89483-7
Imprint: NORTH-HOLLAND
Price: Order form
EUR 71.95
USD 85.95
GBP 47.99
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Last update: 30 Aug 2008
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