Ramsey's theorem and products in the Weihrauch degrees

Damir D Dzhafarov (1) , Jun Le Goh (2) , Denis R Hirschfeldt (3) , Ludovic Patey (4, 5) , Arno Pauly (6)

1 UCONN - University of Connecticut
2 Cornell University [New York]
3 UIC - University of Illinois [Chicago]
4 AGL - Algèbre, géométrie, logique
5 CNRS - Centre National de la Recherche Scientifique
6 Swansea University

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 ($\mathsf{RT}^2_2$) is strictly Weihrauch below the parallel product of the stable Ramsey's theorem for pairs and the cohesive principle ($\mathsf{SRT}^2_2 \times \mathsf{COH}$).

Domaines: Logique [math.LO]

Damir D Dzhafarov, Jun Le Goh, Denis R Hirschfeldt, Ludovic Patey, Arno Pauly. Ramsey's theorem and products in the Weihrauch degrees. Computability, 2020, 9 (2), pp.85--110. ⟨10.3233/COM-180203⟩. ⟨hal-01888805⟩