Table of Contents

COMPUTABILITY, AND UNSOLVABLE PROBLEMS: Hilbert and the Origins of Computability Theory. Models of Computability and the Church-Turing Thesis. Language, Proof and Computable Functions. Coding, Self-Reference and Diagonalisation. Enumerability and Computability. The Search for Natural Examples of Incomputable Sets. Comparing Computability. Gödel's Incompleteness Theorem. Decidable and Undecidable Theories. INCOMPUTABILITY AND INFORMATION CONTENT: Computing with Oracles. Nondeterminism, Enumerations and Polynomial Bounds. MORE ADVANCED TOPICS: Post's Problem: Immunity and Priority. The Computability of Theories. Forcing and Category. Applications of Determinacy. Computability and Structure.

Reviews

"A very nice volume indeed. Although primarily a textbook, it lives up to the author's aim to have 'plenty here to interest and inform everyone, from the beginner to the expert.' … Cooper writes in an informal style, emphasizing the ideas underlying the techniques. All the standard topics and classic results are here. … Students will find useful pointers to the literature and an abundance of exercises woven into the text."
- Zentralblatt MATH, 1041
"[It] provides not only a reference repository of well-crafted proofs or proof-outlines for a large number of basic and beyond-basic facts in several areas of computability theory, but can also serve well as the textual basis for a course on the subject…"
- Mathematical Reviews, 2005h