Todorčević has shown that there is a ccc extension M in which MAω1 + 2ω = ω2 holds and also in which the partition relation ωi → (ω1,α)2 holds for every denumerable ordinal α. We show that the partition relation for triples ω1 → (ω2 + 1, 4)3 holds in the model M, and hence by absoluteness this is a theorem in ZFC.
Bibliographical noteFunding Information:
NSERC Grant No. A5198 and NSF Grant MCS 830361.