Indicator arguments and the strength of Ramsey's theorem

Keita Yokoyama, JAIST. Part of the logic seminar series.

The indicator argument is introduced by Paris in 1970\'s. It is a strong tool to analyze the proof-theoretic strength of axioms in arithmetic by connecting finite and infinite combinatorial principles.It plays a key role in the proof of the conservation result for Ramsey's theorem for pairs and two colors. In this talk, I will consider several variations of indicator arguments, and study the first-order strength of Ramsey's theorem for pairs and other combinatorial principles.

Keita Yokoyama, JAIST