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

Peter A. Cholak; Damir D. Dzhafarov; Denis R. Hirschfeldt; Ludovic Patey

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arXiv · 1901.10326

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

Peter A. Cholak·Damir D. Dzhafarov·Denis R. Hirschfeldt·Ludovic Patey

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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.

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Peter A. Cholak, Damir D. Dzhafarov, Denis R. Hirschfeldt, Ludovic Patey. 2019-01-29. Some results concerning the $\mathsf{SRT}^2_2$ vs. $\mathsf{COH}$ problem. https://arxiv.org/abs/1901.10326

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