COH, SRT22, and multiple functionals
Damir D. Dzhafarov, Ludovic Patey · Computability · 2020
We prove the following result: there is a family [Formula: see text] of subsets of ω such that for every stable coloring [Formula: see text] 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 [Formula: see text] to an infinite cohesive set for R. This provides a partial answer to a question in computable combinatorics, whether [Formula: see text] is omnisciently computably reducible to [Formula: see text].