The first book surveying the history and ideas behind reverse mathematics Reverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
Stillwell's book is self-contained and includes much background material in analysis, mathematical logic, combinatorics, and computability. I heartily commend this very readable and accessible book. -Stephen Simpson, Vanderbilt University Filling an important niche, this book gives readers a good picture of the basics of reverse mathematics while suggesting several directions for further reading and study. -Denis Hirschfeldt, University of Chicago Stillwell carefully situates the field in the broader context of the history of mathematics and its foundations, and does a fine job of making the whole endeavor accessible to a general mathematical audience. -Jeremy Avigad, Carnegie Mellon University The field has been due for a general treatment accessible to undergraduates and to mathematicians in other areas. . . . With Reverse Mathematics, John Stillwell provides exactly that kind of introduction. -Carl Mummert, Notices of the American Mathematical Society