2020.10.16 Yudai Suzuki
Hindman’s theorem and Gowers’ theorem in second order arithmetic

Date/Time: October 16, 2020 (Friday) / 15:00  16:00.

Speaker: Yudai Suzuki (東北大学大学院 理学研究科)

Venue: Room 802, Science Complex A, Tohoku University.

Abstract: Hindman’s theorem is a Ramseytype theorem which was proved by N. Hindman. GalvinGlazer gave a proof of it which uses an ultrafilter on \(\mathbb{N}\) with specific properties. In the context of reverse mathematics, GalvinGlazer’s proof was analysed by H. Towsner, and it was shown that the proof can be formalized in \(\Pi^1_1\)\(\text{TR}_0\).
Gowers’ theorem is a generalization of Hindman’s theorem which is provable in a similar way of GalvinGlazer’s proof of Hindman’s theorem. In this talk, we will compare those proofs and then consider how the proof of Gowers’ theorem be formalized in second order arithmetic.