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We provide a much shorter proof of the following partition theorem of P. Erd˝ os and R. Rado: If X is an uncountable linear order into which neither ω 1 nor ω * 1 embeds, then X → (α, 4) 3 for every ordinal α < ω + ω. We also provide two counterexamples to possible generalizations of this theorem, one of which answers a question of E. C. Milner and K.… (More)

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