Ramsey's theorem and products in the Weihrauch degrees

TL;DR

This paper investigates the structure of the Weihrauch lattice concerning combinatorial principles related to Ramsey's theorem, revealing new relationships between these principles and their computational strengths.

Contribution

It provides new insights into the Weihrauch degrees of Ramsey-type principles, including answering an open question about the relative strength of RT^2_2.

Findings

RT^2_2 is strictly below the product of SRT^2_2 and COH in the Weihrauch lattice.

The paper clarifies the computational complexity relationships among Ramsey's theorem variants.

It advances understanding of the Weihrauch degrees of combinatorial principles.

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 ($\mathsf{SRT}^2_2 \times \mathsf{COH}$).