Computability Theory

Offers a concise introduction to the results and techniques of contemporary computability theory Reflects modern developments in treatment and subject matter in this fundamentally important area Provides an accessible guide to the direction of current research Includes discussions of automporphisms, Turing degrees, and generalized computability theory Recent work in computability theory has focused on automorphisms and promises to have far-reaching mathematical, scientific, and philosophical consequences. Written by a leading researcher, this is a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results and a guide to the direction of current research in the field. It includes both the standard material for a first course in computability and more advanced looks at Turing degrees, forcing, automorphisms, and determinacy. The final chapter explores a variety of computability applications to mathematics and science, including recent work on the Mandelbrot and Julia sets.