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{\bf Albin L. Jones}
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{\bf A short proof of a partition relation for triples }
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We provide a much shorter proof of the following partition theorem
of P.~Erd\H{o}s and R.~Rado: If~$X$ is an uncountable linear order
into which neither~$\omega_1$ nor~$\omega_1^{*}$ embeds, then $X \to
(\alpha, 4)^{3}$ for every ordinal~$\alpha < \omega + \omega$. We
also provide two counterexamples to possible generalizations of this
theorem, one of which answers a question of E.~C.~Milner and
K.~Prikry.
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