Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A general Ramsey product theorem

Authors: R. L. Graham and J. H. Spencer
Journal: Proc. Amer. Math. Soc. 73 (1979), 137-139
MSC: Primary 05C55
MathSciNet review: 512076
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Call a family $ \mathcal{F}$ of subsets of a set U Ramsey if no partition of U into finitely many parts can split every $ F \in \mathcal{F}$. We show that under very general conditions an arbitrary collection of Ramsey families in fact has a much stronger uniform Ramsey property.

References [Enhancements On Off] (What's this?)

  • [1] N. G. de Bruijn and P. Erdös, A colour problem for infinite graphs and a problem in the theory of relations, Indag. Math. 13 (1951), 371-373. MR 0046630 (13:763g)
  • [2] R. L. Graham and B. L. Rothschild, A short proof of van der Waerden's theorem on arithmetic progressions, Proc. Amer. Math. Soc. 42 (1974), 385-386. MR 0329917 (48:8257)
  • [3] R. Rado, Studien zur Kombinatorik, Math. Z. 36 (1933), 424-480. MR 1545354
  • [4] B. L. van der Waerden, Beweis einer Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212-216.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05C55

Retrieve articles in all journals with MSC: 05C55

Additional Information

Keywords: Ramsey's Theorem, partitions
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society