2019/05/01 by Dzhafarov, Damir, Patey, Ludovic
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1905.00321
We prove the following result: there is a family R = ⟨ R0,R1,… ⟩ 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 extends the current best partial results towards the SRT22 vs. COH problem in reverse mathematics, and is also a partial result towards the resolution of several related problems, such as whether COH is omnisciently computably reducible to SRT22.