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Partitioning triples and partially ordered sets

Authors:	Albin L Jones

Institution:	Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142

Abstract:	We prove that if is a partial order and $P \to (\omega)^1_\omega$ , then (a) $P \to (\omega + \omega + 1, 4)^3$ , and (b) $P \to (\omega + m, n)^3$ for each $m, n < \omega$ . Together these results represent the best progress known to us on the following question of P. Erdos and others. If $P \to (\omega)^1_\omega$ , then does $P \to (\alpha, n)^3$ for each $\alpha < \omega_1$ and each $n < \omega$ ?

Keywords:	Countable ordinals non-special tree partial order Ramsey theory triples

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