Ramsey's Theorem and Products in the Weihrauch Degrees

by Damir D. Dzhafarov, Jun Le Goh Denis R. Hirschfeldt, Ludovic Patey, and Arno Pauly

Status: published in Computability 9 (2020) 85 - 110

Availability: online journal version and preprint

Abstract. We study the positions in the Weihrauch lattice of parallel products of various combinatorial principles related to Ramsey's theorem. Among other results, we obtain an answer to a question of Brattka, by showing that Ramsey's theorem for pairs (RT22) is strictly Weihrauch below the parallel product of the stable Ramsey's theorem for pairs and the cohesive principle (SRT22 × COH).