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Other titles in the London Mathematical Society Lecture Notes series:
Computability, Enumerability, Unsolvability: Directions in Recursion Theory (London Mathematical Society Lecture Note)by S. B. Cooper
Synopses & Reviews
The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.
Book News Annotation:
A series of 15 papers commemorating the Leeds Recursion Theory Year, 1993-94, combining background and introductory material with recent developments such as solutions to the stubborn problems of definability, decidability, and automorphisms. Array nonrecursive degrees and genericity, relativization of structures arising from computability theory, and the Medvedev lattice of degrees of difficulty are among the topics. Also includes several pages of open questions, and an e-mail address to send answers. No index.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
It is just over 60 years since Alan Turing, Alonzo Church and Kurt Gödel showed the existence of fundamental undecidable problems in mathematics. The contributions in this book provide an up-to-date overview of current ideas and methods in the pure mathematical foundations of computability theory, the discipline which grew out of their pioneering work. A number of the articles contain introductory and background material, making this volume an invaluable resource for specialists and non-specialists alike.
Provides a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory.
Contributions from the Leeds recursion theory year, at the interface between logic and theoretical computer science.
Table of Contents
Minimal degrees below O' and the jump operator B. Cooper; Boolean algebras and ideals associated with the lattice of r.e. sets L. Harrington; Codable sets L. Harrington and R. Soare; Subrecursion theories A. Heaton and S. Wainer; An appraoch to lattice embaddings M. Lerman; A hierarchy of domains with totality, but without density D. Norman; Inductive inference P. Odifreddi; The discontinuity of the Slaman-Soare phenomenon X. YI; Recursive enumerability M. Arslanov; Resource bounded gereicity concepts K. Ambos-Spies; The Medvedev lattice of degrees of difficulty A. Sorbi; On the number of countable models II G. Sacks.
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