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Some results concerning the $$\mathsf{SRT}_2^2$$ vs. $$\mathsf{COH}$$ problem. (English) Zbl 07271573
Summary: 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.
##### MSC:
 03D Computability and recursion theory
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