an:07271557
Zbl 07271557
Dzhafarov, Damir D.; Goh, Jun Le; Hirschfeldt, Denis R.; Patey, Ludovic; Pauly, Arno
Ramsey's theorem and products in the Weihrauch degrees
EN
Computability 9, No. 2, 85-110 (2020).
00453905
2020
j
03D
computable combinatorics; Ramsey theory; computability theory; reverse mathematics
Summary: 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 Weihrauch-incomparable to the parallel product of the stable Ramsey's theorem for pairs and the cohesive principle \((\mathsf{SRT}_2^2 \times \mathsf{COH})\).