Computability Theory

Recent work in computability theory has focused on Turing definability 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 that also serves as a guide to the direction of current research in the field. Computability Theory includes both the standard material for a first course in computability and more advanced looks at Turing degrees, forcing, Turing definability, and determinacy. The final chapter explores a variety of computability applications in mathematics and science.