Strong Reductions between Relatives of the Stable Ramsey's Theorem
David J. Nichols · arXiv (Cornell University) · 2017
A complete analysis is given of the computable reductions that hold between $\mathsf{SRT}^2_2$, $\mathsf{SPT}^2_2$, and $\mathsf{SIPT}^2_2$. In particular, while $\mathsf{D}^2_2\le_{\rm sW}\mathsf{SIPT}^2_2\le_{\rm sW}\mathsf{SPT}^2_2\le_{\rm sW}\mathsf{SRT}^2_2$, it is shown that $\mathsf{SRT}^2_2 ot\le_{\rm sc}\mathsf{SPT}^2_2 ot\le_{\rm sc}\mathsf{SIPT}^2_2 ot\le_{\rm sc}\mathsf{D}^2_2$.