Negative Partition Relations for Ordinals ωωα

For ordinals α, β, and γ, the expression α↛(β, γ)2 means there is a partition of the pairs from α, [α]2=Δ0∪Δ1 such that for any X⊆α, if the order type of X is β then [X]2⊈Δ0 and if the order type of X is γ then [X]2⊈Δ1. It is shown that if α<ω1 is multiplicatively decomposable, then ωα↛(ωα, n)2 for n=4 or n=6, depending on the degree of decomposability of α.