Some results concerning the ${\mathsf{SRT}}_2^2$ vs. $\mathsf{COH}$ problem

Abstract

The ${\mathsf{SRT}}_2^2$ vs.\ $\mathsf{COH}$ problem is a central problem in computable combinatorics and reverse mathematics, asking whether every Turing ideal that satisfies the principle ${\mathsf{SRT}}_2^2$ also satisfies the principle $\mathsf{COH}$. This paper is a contribution towards further developing some of the main techniques involved in attacking this problem. We study several principles related to each of ${\mathsf{SRT}}_2^2$ and $\mathsf{COH}$, and prove results that highlight the limits of our current understanding, but also point to new directions ripe for further exploration.