Cohesive sets and rainbows
Abstract
We study the strength of 32, Rainbow Ramsey Theorem for colorings of triples, and prove that + 32 implies neither nor 42. 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 '-recursive sequence (2-bounded coloring of pairs) admits a 3 cohesive set (infinite rainbow).
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