Affiliations: [a] Department of Mathematics, University of Notre Dame, IN, USA. [email protected] | [b] Department of Mathematics, University of Connecticut, CT, USA. [email protected] | [c] Department of Mathematics, University of Chicago, IL, USA. [email protected] | [d] Institut Camille Jordan, Université Claude Bernard Lyon 1, France. [email protected]
Abstract: The SRT22 vs. COH problem is a central problem in computable combinatorics and reverse mathematics, asking whether every Turing ideal that satisfies the principle SRT22 also satisfies the principle 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 SRT22 and COH, and prove results that highlight the limits of our current understanding, but also point to new directions ripe for further exploration.
