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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?)

  • [1] J. Baumgartner and A. Hajnal, A proof (involving Martin's axiom) of a partition relation, Fund. Math. 78 (1973), 193-203. MR 0319768 (47:8310)
  • [2] P. Erdös, A. Hajnal and E. C. Milner, Set mappings and polarized partition relations, Combinatorial Theory and Its Applications. I (Proc. Colloq., Balatonfüred, 1969), Colloq. Math. Soc. János Bolyai, Vol. 4, North-Holland, Amsterdam, 1970, pp. 327-363. MR 0299537 (45:8585)
  • [3] F. Galvin, On a partition theorem of Baumgartner and Hajnal, Infinite and Finite Sets. II (Proc. Colloq., Keszthely, 1973), Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, pp. 711-729. MR 0376355 (51:12531)
  • [4] T. Jech, Set theory, Academic Press, New York, San Francisco and London, 1978. MR 506523 (80a:03062)

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

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