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Transactions of the American Mathematical Society

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A partition relation for Souslin trees

Author: Attila Máté
Journal: Trans. Amer. Math. Soc. 268 (1981), 143-149
MSC: Primary 03E05; Secondary 04A20
MathSciNet review: 628450
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Abstract: The aim of these notes is to give a direct proof of the partition relation Souslin tree $\to (\alpha )_k^2$, valid for any integer $k$ and any ordinal $\alpha < {\omega _1}$. This relation was established by J. E. Baumgartner, who noticed that it follows by a simple forcing and absoluteness argument from the relation ${\omega _1} \to (\alpha )_k^2$, which is a special case of a theorem of Baumgartner and A. Hajnal.

References [Enhancements On Off] (What's this?)

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Keywords: Infinite game, partition relation, Souslin tree
Article copyright: © Copyright 1981 American Mathematical Society