More results in polychromatic Ramsey theory

<p>We study polychromatic Ramsey theory with a focus on colourings of [<em>ω</em> 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 ^<em>ω</em> = <em>ω</em> 2 and ω2→poly(α)2_ℵ0−bdd for every<em>α</em> <<em>ω</em> 2; <strong>(2)</strong> 2 <em>ω</em> = <em>ω</em> 2 and ω2↛^poly(ω1)²_2−bdd.</p>