Description

This book is a collection of advanced research/survey papers by eminent research workers in the Recursion theory. 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. 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. 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). 1. Fundamental methods for connecting recursively enumerable degrees R. I. Soare; 2. A Survey of Non-RE Degrees ≤ 0' D. B. Posner; 3. Degrees of Generic Sets C. G. Jockusch; 4. The Degrees of Unsolvability: Some recent results M. Lerman; 5. Some Constructions in ά-Recursion theory R. Shore; 6. The Recursion theory of the continuous functionals D. Norman; 7. Three aspects of recursive enumerability in higher types G. E. Sacks; 8. Computing in Algebraic Systems J. V. Tucker; 9. Applications of Classical Recursion theory to computer science C. H. Smith; 10. 'Natural' programming languages and complexity measures for subrecursive programming languages: An Abstract Approach D. A. Alton; 11. Complexity Theory with Emphasis on the complexity of logical theories R. E. Ladner.