# Computability Theory

## An Introduction to Recursion Theory

Computability Theory:  An Introduction to Recursion 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 text 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 way.

Audience

Upper-level mathematics and computer science students.

Hardbound, 192 Pages

Published: December 2010

ISBN: 978-0-12-384958-8

## Reviews

• "This textbook on basic computability theory is at the upper-undergraduate level."--Zentralblatt MATH 2012-1243-03057
"Enderton (U. of California, Los Angeles) has written a clear, focused, and surprisingly literate textbook â it is a rare mathematician who is this adept with words â describing the history and theory of recursion theory that will be ideal for one-semester advanced courses in mathematics and computer science. After the concepts and theories are introduced, the equivalence of computable partial function and recursive partial function are demonstrated, in part through proofs of the unsolvability of the halting problem and of the enumeration theorem. Other chapters describe the properties of recursively enumerable sets, the link between computability theory and GÃ¶del's incompleteness theorem, relative computability and degrees of unsolvability, and polynomial time computability. Appendices are included on Mathspeak, countability, and decadic notation."--SciTechBookNews
"Computability is concerned with the question of what computers can do in principle. Since Enderton directly contributed to the very areas that this book covers (computability and computational complexity), he is able to provide a concise and comprehensive firsthand view on the subject. As a scholar in the field, as well as in the history of logic, he frequently includes historical passages when presenting new concepts in the bookâ¦. This is a beautifully written and beautifully printed book.... The book fits perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related areas. It is a lovely, short book that contains great ideas."--Computing Reviews

## Contents

• 1. The Computability Concept;
2. General Recursive Functions;
3. Programs and Machines;
4. Recursive Enumerability;
5. Connections to Logic;
6. Degrees of Unsolvability;
7. Polynomial-Time Computability;
Appendix: Mathspeak;
Appendix: Countability;