Computability theory, reverse mathematics, and combinatorial principles

Abstract:

Computable mathematics and reverse mathematics are closely-related approaches to studying the relative strength of mathematical principles. I will give an introduction to this area of research, drawing my examples mainly from combinatorial principles that live in the part of the reverse-mathematical universe corresponding to arithmetic mathematics, such as versions of Ramsey’s Theorem. There has been a great deal of interest in this line of research in recent years, and I will also discuss recent results and open questions.