Reverse Mathematics

The Reverse Mathematics program classifies theorems of ordinary mathematics in terms of their inherent logical strength. This book provides a complete introduction to the field, emphasizing its relationship with computability and the key techniques used in contemporary research. Many applications, including weak combinatorial principles related to Ramsey's theorem, are covered for the first time in book form. The final part covers alternative approaches including constructive reverse mathematics and uncountable reverse mathematics.

The book is aimed at graduate students and researchers in mathematical logic and related fields. The first part, in particular, will be aimed at graduate students, and will include exercises to make the book suitable for use as a textbook.