Description
Book SynopsisThis book presents mathematical logic from the syntactic point of view, with an emphasis on aspects that are fundamental to computer science. It is an excellent introduction for graduate students and advanced undergraduates interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for professional logicians.
Trade Review'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
'This book by one of the most knowledgeable researchers in the field covers a remarkably broad selection of material without sacrificing depth. Its clear organization and unified approach - focused on a syntactic approach and on the role of computation - make it suitable for a wide range of introductory logic sequences at the upper-level undergraduate and graduate level, as well as a valuable resource for background material in more advanced logic courses.' Denis Hirschfeldt, University of Chicago
'… an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting … this is most certainly a book to make sure your library gets.' Peter Smith, Logic Matters
Table of ContentsPreface; 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.
