A partition relation for Souslin trees
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- 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
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