Recursion Theory, its Generalisations and Applications (London Mathematical Society Lecture Note Series, Series Number 45)

Recursion theory - now a well-established branch of pure mathematics, having grown rapidly over the last 35 years - deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines. The theory grew out of, and is usually still regarded, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR). CONTENTS......Page 5 Preface......Page 7 List of Participants......Page 8 Fundamental Methods for Constructing Recursively Enumerable Degrees......Page 9 A Survey of Non-RE Degrees < 0'......Page 60 Degrees of Generic Sets......Page 118 The Degrees of Unsolvability: Some Recent Results......Page 148 Some Constructions in a-Recursion Theory......Page 166 The Recursion Theory of the Continuous Functionals......Page 179 Three Aspects of Recursive Enumerability in Higher Types......Page 192 Computing in Algebraic Systems......Page 223 Applications of Classical Recursion Theory to Computer Science......Page 244 "Natural" Programming Languages and Complexity Measures for Subrecursive Programming Languages: An Abstract Approach......Page 256 Complexity Theory with Emphasis on the Complexity of Logical Theories......Page 294 Edited By F. R. Drake And S. S. Wainer. Includes Bibliographical References.