Computability Theory

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CRC Press, Nov 17, 2003 - Mathematics - 424 pages
2 Reviews
Computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications. Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences.

Written by a leading researcher, Computability Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level.

The book includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science.

Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable and lively way.
 

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Contents

Hilbert and the Origins of Computability Theory
3
Models of Computability and the ChurchTuring Thesis
11
Language Proof and Computable Functions
45
Coding SelfReference and the Universal Turing Machine
61
Enumerability and Computability
69
The Search for Natural Examples of Incomputable Sets
87
Comparing Computability and the Ubiquity of Creative Sets
101
Godels Incompleteness Theorem
117
Nondeterminism Enumerations and Polynomial Bounds
173
Immunity and Priority
219
Forcing and Category
273
Applications of Determinacy
311
The Computability of Theories
321
Computability and Structure
343
Further Reading
383
Index
389

Decidable and Undecidable Theories
127
Computing with Oracles
139

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