Mathematical Logic and Computation

Jeremy Avigad is Professor in the Department of Philosophy and the Department of Mathematical Sciences at Carnegie Mellon University. His research interests include mathematical logic, formal verification, automated reasoning, and the philosophy and history of mathematics. He is the Director of the Charles C. Hoskinson Center for Formal Mathematics at Carnegie Mellon University.

• Preface; 1. Fundamentals; 2. Propositional Logic; 3. Semantics of Propositional Logic; 4. First-Order Logic; 5. Semantics of First-Order Logic; 6. Cut Elimination; 7. Properties of First-Order Logic; 8. Primitive Recursion; 9. Primitive Recursive Arithmetic; 10. First-Order Arithmetic; 11. Computability 12. Undecidability and Incompleteness; 13. Finite Types; 14. Arithmetic and Computation; 15. Second-Order Logic and Arithmetic; 16. Subsystems of Second-Order Arithmetic; 17. Foundations; Appendix; References; Notation; Index.

'Avigad provides a much needed introduction to mathematical logic that foregrounds the role of syntax and computability in our understanding of consistency and inconsistency. The result provides a jumping off point to any of the fields of modern logic, not only teaching the technical groundwork, but also providing a window into how to think like a logician.' Henry Towsner, University of Pennsylvania