Strong Reductions between Relatives of the Stable Ramsey's Theorem

Abstract

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 ${\mathsf{D}}_2^2{\le }_{\mathrm{sW}}{\mathsf{SIPT}}_2^2{\le }_{\mathrm{sW}}{\mathsf{SPT}}_2^2{\le }_{\mathrm{sW}}{\mathsf{SRT}}_2^2$, it is shown that ${\mathsf{SRT}}_2^2/{\le }_{\mathrm{sc}}{\mathsf{SPT}}_2^2/{\le }_{\mathrm{sc}}{\mathsf{SIPT}}_2^2/{\le }_{\mathrm{sc}}{\mathsf{D}}_2^2$.