Sole Distributors for the Usa and Canada, Elsevier Science Pub. Co. (1989)

Abstract
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.
Keywords Recursion theory
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Reprint years 1992
Buy this book $53.76 used (45% off)   $71.89 new (27% off)   Amazon page
Call number QA9.6.O35 1989
ISBN(s) 0444872957   0444894837   9780444872951   9780444894830
DOI 10.2307/2274492
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The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
On Interpreting Chaitin's Incompleteness Theorem.Panu Raatikainen - 1998 - Journal of Philosophical Logic 27 (6):569-586.
A Cohesive Set Which is Not High.Carl Jockusch & Frank Stephan - 1993 - Mathematical Logic Quarterly 39 (1):515-530.

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