The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs
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 SRT22 implies DNR over RCA0 but COH does not, and answer a question of Mileti by showing that every computable stable 2-coloring of pairs has an incomplete 02 infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT22 does not imply RT22.
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