More on partitioning triples of countable ordinals
HTML articles powered by AMS MathViewer
- by Albin L. Jones PDF
- Proc. Amer. Math. Soc. 135 (2007), 1197-1204
Abstract:
Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal $m$ the first class of the partition contains all triples from a set of type $\omega + m$, or for each finite ordinal $n$ the second class of the partition contains all triples of an $n$-element set. That is, we prove that $\omega _1 \to (\omega + m, n)^3$ for each pair of finite ordinals $m$ and $n$.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. Erdös and R. Rado, A partition calculus in set theory, Bull. Amer. Math. Soc. 62 (1956), 427–489. MR 81864, DOI 10.1090/S0002-9904-1956-10036-0
- 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
- A. Hajnal, Some results and problems on set theory, Acta Math. Acad. Sci. Hungar. 11 (1960), 277–298 (English, with Russian summary). MR 150044, DOI 10.1007/BF02020945
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
- A. Jones, Some results in the partition calculus, Ph.D. thesis, Dartmouth College, June 1999.
- Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1983. An introduction to independence proofs; Reprint of the 1980 original. MR 756630
- E. C. Milner and K. Prikry, A partition theorem for triples, Proc. Amer. Math. Soc. 97 (1986), no. 3, 488–494. MR 840635, DOI 10.1090/S0002-9939-1986-0840635-8
- E. C. Milner and K. Prikry, A partition relation for triples using a model of Todorčević, Discrete Math. 95 (1991), no. 1-3, 183–191. Directions in infinite graph theory and combinatorics (Cambridge, 1989). MR 1141938, DOI 10.1016/0012-365X(91)90336-Z
- F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264–286.
- W. Sierpiński, Sur un problème de la théorie des relations, Annali E. Scuola Normale Superiore de Pisa Ser. 2 2 (1933), 285–287.
- Jack H. Silver, A large cardinal in the constructible universe, Fund. Math. 69 (1970), 93–100. MR 274278, DOI 10.4064/fm-69-1-93-100
- Stevo Todorčević, Forcing positive partition relations, Trans. Amer. Math. Soc. 280 (1983), no. 2, 703–720. MR 716846, DOI 10.1090/S0002-9947-1983-0716846-0
- Stevo Todorčević, Partition relations for partially ordered sets, Acta Math. 155 (1985), no. 1-2, 1–25. MR 793235, DOI 10.1007/BF02392535
Additional Information
- Albin L. Jones
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142
- Address at time of publication: 2153 Oakdale Rd., Pasadena, Maryland 21122-5715
- MR Author ID: 662270
- Email: alj@mojumi.net
- Received by editor(s): March 1, 2005
- Received by editor(s) in revised form: October 25, 2005
- Published electronically: September 26, 2006
- Additional Notes: The author would like to thank the University of Kansas for its support of this research.
- Communicated by: Julia Knight
- © Copyright 2006 by Albin L. Jones
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1197-1204
- MSC (2000): Primary 03E05, 04A20; Secondary 05A18, 05D10
- DOI: https://doi.org/10.1090/S0002-9939-06-08538-8
- MathSciNet review: 2262926