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 Ramsey-type theorem which was proved by N. Hindman. Galvin-Glazer gave a proof of it which uses an ultrafilter on \(\mathbb{N}\) with specific properties. In the context of reverse mathematics, Galvin-Glazer’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 Galvin-Glazer’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.