Mathematical Logic and Computation

Description

This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf.

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.

'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