Date of Original Version
The final publication is available at Springer via http://dx.doi.org/10.2478/s11533-012-0037-3
Abstract or Description
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.
Central European Journal of Mathematics, 10, 3, 1104-1016.