More on partitioning triples of countable ordinals

Jones, Albin

doi:10.1090/S0002-9939-06-08538-8

More on partitioning triples of countable ordinals
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by Albin L. Jones PDF

Proc. Amer. Math. Soc. 135 (2007), 1197-1204

Abstract:

Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal $m$ the first class of the partition contains all triples from a set of type $\omega + m$, or for each finite ordinal $n$ the second class of the partition contains all triples of an $n$-element set. That is, we prove that $\omega _1 \to (\omega + m, n)^3$ for each pair of finite ordinals $m$ and $n$.

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