Strong reductions and combinatorial principles
Damir D. Dzhafarov · arXiv (Cornell University) · 2015
This paper is a contribution to the growing investigation of strong reducibilities between $Π^1_2$ statements of second-order arithmetic, viewed as an extension of the traditional analysis of reverse mathematics. We answer several questions of Hirschfeldt and Jockusch (to appear) about uniform and strong computable reductions between various combinatorial principles related to Ramsey's theorem for pairs. Among other results, we establish that the principle $\mathsf{SRT}^2_2$ is not uniformly or strongly computably reducible to $\mathsf{D}^2_{