 |
|
| CLASSICAL RECURSION THEORY
| |
| | |
|
|
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 details |
Paperback, 0 pages, publication date: FEB-1992
ISBN-13: 978-0-444-89483-0
ISBN-10: 0-444-89483-7
Imprint: NORTH-HOLLAND
|
| Price and Ordering |
Price:
EUR 65.95
USD 90.95
GBP 56
|  |
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
|
See also information about conditions of sale & ordering procedures, and links to our regional sales offices.
|
050/500
Last update: 4 Sep 2009
|
|
| |
| | |
|
|
| |
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company