The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.

Preliminaries 1. Propositional Logic 2. Structures and First-Order Logic 3. Proof Theory 4. Properties of First-Order Logic 5. First-Order Theories 6. Models of Countable Theories 7. Computability and Complexity 8. The Incompleteness Theorems 9. Beyond First-Order Logic 10. Finite Model Theory Bibliography Index

Shawn Hedman , Department of Mathematics, Florida Southern College

'a clear and unifying treatment of fundamental concepts underlying Computer Sciences and Foundations of Mathematics' Professor Boris Zilber (Professor of Mathematical Logic, University of Oxford)