论文信息 - Cohesive sets and rainbows

Cohesive sets and rainbows

Abstract We study the strength of RRT 2 3 , Rainbow Ramsey Theorem for colorings of triples, and prove that RCA 0 + RRT 2 3 implies neither WKL 0 nor RRT 2 4 . 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 low 3 cohesive set (infinite rainbow).

Wei Wang

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