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arXiv · 1408.2897

The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs

Denis R. Hirschfeldt·Carl G. Jockusch·Bjørn Kjos-Hanssen·Steffen Lempp·Theodore A. Slaman
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Abstract

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 $Δ^0_2$ 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$^2_2$.

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Denis R. Hirschfeldt, Carl G. Jockusch, Bjørn Kjos-Hanssen, Steffen Lempp, Theodore A. Slaman. 2014-08-13. The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs. https://doi.org/10.1142/9789812796554_0008

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