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arXiv · 1804.10968

Ramsey's theorem and products in the Weihrauch degrees

Damir D. Dzhafarov·Jun Le Goh·Denis R. Hirschfeldt·Ludovic Patey·Arno Pauly
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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 ($\mathsf{RT}^2_2$) is strictly Weihrauch below the parallel product of the stable Ramsey's theorem for pairs and the cohesive principle ($\mathsf{SRT}^2_2 \times \mathsf{COH}$).

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Damir D. Dzhafarov, Jun Le Goh, Denis R. Hirschfeldt, Ludovic Patey, Arno Pauly. 2018-04-29. Ramsey's theorem and products in the Weihrauch degrees. https://arxiv.org/abs/1804.10968

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