Giovanni Soldà (Ghent University)
Location: MALL 1
Title: On the strength of some first-order problems corresponding to Ramseyan principles
Given a represented space $X$, we say that a partial multifunction $f$ with $\operatorname{dom}(f) ⊆ X$ is first-order if its codomain is the set of the natural numbers. In this talk, we will study, from the point of view of Weihrauch reducibility, some first-order problems corresponding to Ramseyan combinatorial principles. We will start by analyzing some problems that can be seen naturally as first-order: more specifically, we study some principles whose strengths, from a reverse mathematical perspective, lie around $IΣ_0^2$. We will then move to study the first-order part of problems which cannot be presented as first-order ones. The first-order part operator was introduced by Dzhafarov, Solomon and Yokoyama in unpublished work, and it has already proved to be a valuable tool to gauge the strengths of various problems according to Weihrauch reducibility. After giving some technical results on this operator, we will focus on the first-order part of Ramsey's theorem for pairs, presenting various results on the position of its degree in the Weihrauch lattice. The results presented are joint work with Arno Pauly, Pierre Pradic, and Manlio Valenti.