Computability Theory: Introduction to Recursion Theory

Computability Theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930s. This theory includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, and subrecursive hierarchy classifications.

Recent work in computability theory has focused on Turing definability and promises to have far-reaching mathematical, scientific, and philosophical consequences.

These texts provide concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context.

The texts include both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. They also explore a variety of computability applications to mathematics and science.

These are invaluable texts, references, and guides to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way.