Full name: Quentin Le Houerou
Affiliation: Paris-East Créteil University, LACL laboratory
Title of the talk: Π^0_4 conservation of Ramsey's theorem for pairs
Abstract: The search for the first-order part of Ramsey's theorem for pairs and two colors (RT^2_2) has been a long-standing question in the field of reverse mathematics. RT^2_2 is known to be provable using Σ^0_2 induction but is strictly weaker than it. It also implies a statement called Σ^0_2-collection (BΣ^0_2). However, whether RT^2_2 is conservative over the base theory RCA_0 + BΣ^0_2 for arithmetic statements remains an open question.
In their 2016 article, Ludovic Patey and Keita Yokoyama showed that RT^2_2 was Π^0_3 conservative over the base theory RCA_0 + BΣ^0_2. In this talk, we provide a sketch of an improvement of that result using an elaboration of the method of indicators, by showing that RT^2_2 is even Π^0_4 conservative over RCA_0 + BΣ^0_2.
This is joint work with Ludovic Levy Patey and Keita Yokoyama.