The Strength of Some Combinatorial Principles Related to Ramsey's   Theorem for Pairs
  We study the reverse mathematics and computability-the\-o\-re\-tic strength of (stable) Ramsey's Theorem for pairs and the related principles COH and DNR. We show that SRT$^2_2$ implies DNR over RCA$_0$ but COH does not, and answer a question of Mileti by showing that every computable stable $2$-coloring of pairs has an incomplete $\Delta^0_2$ infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT$^2_2$ does not imply RT$^2_2$. 
Denis R. Hirschfeldt, Carl G. Jockusch, Bj{\o}rn Kjos-Hanssen, Steffen   Lempp, and Theodore A. Slaman
math.LO