Classical Recursion Theory

The Theory of Functions and Sets of Natural Numbers

By: Piergiorgio Odifreddi

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Paperback | 4 February 1992 | Edition Number 2

At a Glance

Paperback
692 Pages

Edition Type
New edition

Dimensions(cm)
23.5 x 15.88 x 3.18

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$241.75

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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.

Industry Reviews

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 fur 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

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Science Physics Set Theory Computing & I.T.Computer Science Computer Architecture & Logic Design

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
Table of Contents provided by Publisher. All Rights Reserved.

Classical Recursion Theory

The Theory of Functions and Sets of Natural Numbers

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

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