A partition theorem for triples

Milner, E. C.; Prikry, K.

doi:10.1090/S0002-9939-1986-0840635-8

A partition theorem for triples
HTML articles powered by AMS MathViewer

by E. C. Milner and K. Prikry

Proc. Amer. Math. Soc. 97 (1986), 488-494

DOI: https://doi.org/10.1090/S0002-9939-1986-0840635-8

PDF | Request permission

Abstract:

Consider a partition of triples of enumerable ordinals into two classes. We show that either for each natural number $k$, the first class contains all triples from a set of type $\omega + k$, or the second class contains all triples of a four element set.

References

James E. Baumgartner, A new class of order types, Ann. Math. Logic 9 (1976), no. 3, 187–222. MR 416925, DOI 10.1016/0003-4843(76)90001-2
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
Ben Dushnik and E. W. Miller, Partially ordered sets, Amer. J. Math. 63 (1941), 600–610. MR 4862, DOI 10.2307/2371374

Combinatorial set theory

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), Vols. I, II, III, 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
Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132