Classical recursion theory the theory of functions and sets of natural numbers. [Volume 1

1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to effective computability and their relations with computers and programming languages; a discussion of Church's thesis; a modern solution to Post's problem; global properties of Turing degrees; and a complete algebraic characterization of many-one degrees. Included are a number of applications to logic (in particular Gödel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation. Read more... Abstract: Includes a number of applications to logic (in particular Godel's theorems) and to computer science, for which Recursion Theory provides the theoretical foundation. This book presents a comprehensive reference for the subject starting from first principles. Read more... Content: Front Cover Classical Recursion Theory: The Theory of Functions and Sets of Natural Numbers Copyright Page Foreword Preface Preface to the Second Edition Contents Introduction Chapter I. Recursiveness and Computability Chapter II. Basic Recursion Theory Chapter III. Post's Problem and Strong Reducibilities Chapter IV. Hierarchies and Weak Reducibilities Chapter V. Turing Degrees Chapter VI. Many-One and Other Degrees Bibliography Notation Index Subject Index.