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| CLASSICAL RECURSION THEORY, VOLUME II
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 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, 143
Description
Volume II of Classical Recursion Theory describes the universe from a local (bottom-up
or synthetical) point of view, and covers
the whole spectrum, from the
recursive to the arithmetical sets.
The first half of the book provides a detailed picture of the computable
sets from the perspective of Theoretical Computer Science. Besides giving a
detailed description of the theories of abstract Complexity
Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity
classes, ranging from small time and
space bounds to the elementary functions,
with a particular attention to polynomial time and space computability. It also
deals with
primitive recursive functions and larger classes, which are of
interest to the proof theorist.
The second half of the book starts
with the classical theory of recursively
enumerable sets and degrees, which constitutes the core of Recursion or
Computability Theory.
Unlike other texts, usually confined to the Turing
degrees, the book covers a variety of other strong reducibilities, studying
both their
individual structures and their mutual relationships. The last
chapters extend the theory to limit sets and arithmetical sets. The volume
ends with the first textbook treatment of the enumeration degrees, which
admit a number of applications from algebra to the Lambda Calculus.
The book is a valuable source of information for anyone interested in
Complexity and Computability Theory. The student will appreciate
the detailed
but informal account of a wide variety of basic topics, while the specialist
will find a wealth of material sketched in
exercises and asides. A massive
bibliography of more than a thousand titles completes the treatment on the
historical side.
Contents
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. ε0-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.
| Bibliographic details |
Hardbound, publication date: SEP-1999
ISBN-13: 978-0-444-50205-6
ISBN-10: 0-444-50205-X
Imprint: NORTH-HOLLAND
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| Price and Ordering |
Price:
GBP 106
USD 181
EUR 159
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Last update: 26 Sep 2008
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