More results in polychromatic Ramsey theory
journal contributionposted on 2012-02-01, 00:00 authored by Uri Abraham, James CummingsJames Cummings
We study polychromatic Ramsey theory with a focus on colourings of [ω 2]2. We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2 ω = ω 2 and ω2→poly(α)2ℵ0−bdd for everyα <ω 2; (2) 2 ω = ω 2 and ω2↛poly(ω1)22−bdd.