Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A partition relation for Souslin trees
HTML articles powered by AMS MathViewer

by Attila Máté PDF
Trans. Amer. Math. Soc. 268 (1981), 143-149 Request permission

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
  • 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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 03E05, 04A20
  • Retrieve articles in all journals with MSC: 03E05, 04A20
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 268 (1981), 143-149
  • MSC: Primary 03E05; Secondary 04A20
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0628450-1
  • MathSciNet review: 628450