General Recursion Theory An Axiomatic Approach Perspectives in Logic Series

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Perspectives in Logic series, Jens E. Fenstad takes an axiomatic approach to present a unified and coherent account of the many and various parts of general recursion theory. The main core of the book gives an account of the general theory of computations. The author then moves on to show how computation theories connect with and unify other parts of general recursion theory. Some mathematical maturity is required of the reader, who is assumed to have some acquaintance with recursion theory. This book is ideal for a second course in the subject.

Pons Asinorum; On the choice of correct notations for general theory; Part I. General Theory: 1. General theory: combinatorial part; 2. General theory: subcomputations; Part II. Finite Theories: 3. Finite theories on one type; 4. Finite theories on two types; Part III. Infinite Theories: 5. Admissible prewellorderings; 6. Degree structure; Part IV. Higher Types: 7. Computations over two types; 8. Set recursion and higher types; References; Notation; Author index; Subject index.

Jens E. Fenstad works in the Department of Mathematics at the University of Oslo.