Computability, Enumerability, Unsolvability

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.

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.