COH, SRT 2 2 , and multiple functionals

DOI Web Site 1 Citations
  • Damir D. Dzhafarov
    Department of Mathematics, University of Connecticut, CT, U.S.A.. damir@math.uconn.edu
  • Ludovic Patey
    Institut Camille Jordan, Université Claude Bernard Lyon 1, France. ludovic.patey@computability.fr

Abstract

<jats:p>We prove the following result: there is a family R = ⟨ R 0 , R 1 , … ⟩ of subsets of ω such that for every stable coloring c : [ ω ] 2 → k hyperarithmetical in R and every finite collection of Turing functionals, there is an infinite homogeneous set H for c such that none of the finitely many functionals map R ⊕ H to an infinite cohesive set for R. This provides a partial answer to a question in computable combinatorics, whether COH is omnisciently computably reducible to SRT 2 2 .</jats:p>

Journal

  • Computability

    Computability 10 (2), 111-121, 2021-04-16

    IOS Press

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