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arXiv · 1303.3329

Cohesive sets and rainbows

Wei Wang
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Abstract

We study the strength of $\RRT^3_2$, Rainbow Ramsey Theorem for colorings of triples, and prove that $\RCA + \RRT^3_2$ implies neither $\WKL$ nor $\RRT^4_2$. To this end, we establish some recursion theoretic properties of cohesive sets and rainbows for colorings of pairs. We show that every sequence (2-bounded coloring of pairs) admits a cohesive set (infinite rainbow) of non-PA Turing degree; and that every $\emptyset'$-recursive sequence (2-bounded coloring of pairs) admits a $\low_3$ cohesive set (infinite rainbow).

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Wei Wang. 2013-03-14. Cohesive sets and rainbows. https://doi.org/10.1016/j.apal.2013.06.002

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