Computability, Unsolvability, Randomness

This book gives a thorough development of the foundations of computability, from the definition of Turing machines up to finite injury priority arguments. Key topics include relative computability, and computably enumerable sets, those which can be effectively listed but not necessarily effectively decided, such as the theorems of Peano arithmetic.

The author exposits Turing's 1936 theory of computability and unsolvability, as subsequently developed by Kleene and Post. This theory is of the essence in theoretical computer science and in the study of unsolvable mathematical problems. Second, it provides an introductory account of a research area which is currently very active: algorithmic randomness and Kolmogorov complexity.