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...