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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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A partition relation for Souslin trees
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by Attila Máté PDF
Trans. Amer. Math. Soc. 268 (1981), 143-149 Request permission


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.
  • J. Baumgartner and A. Hajnal, A proof (involving Martin’s axiom) of a partition relation, Fund. Math. 78 (1973), no. 3, 193–203. MR 319768, DOI 10.4064/fm-78-3-193-203
  • P. Erdős, A. Hajnal, and E. C. Milner, Set mappings and polarized partition relations, Combinatorial theory and its applications, I (Proc. Colloq., Balatonfüred, 1969) North-Holland, Amsterdam, 1970, pp. 327–363. MR 0299537
  • F. Galvin, On a partition theorem of Baumgartner and Hajnal, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. II, Colloq. Math. Soc. János Bolyai, Vol. 10, North-Holland, Amsterdam, 1975, pp. 711–729. MR 0376355
  • Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 268 (1981), 143-149
  • MSC: Primary 03E05; Secondary 04A20
  • DOI:
  • MathSciNet review: 628450