More results in polychromatic Ramsey theory

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)2_ℵ0−bdd for everyα <ω 2; (2) 2 ω = ω 2 and ω2↛^poly(ω1)²_2−bdd.