Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  757.05010
Autor:  Blass, Andreas; Erdös, Paul; Taylor, Alan
Title:  Diverse homogeneous sets. (In English)
Source:  J. Comb. Theory, Ser. A 59, No.2, 312-317 (1992).
Review:  Let \omega be the set of natural numbers, and [\omega]2 the set of two-element subsets of \omega. A set H\subseteq\omega is said to be diverse with respect to a partition \pi of \omega if at least two pieces of \pi have an infinite intersection with H. A family of partitions of \omega has the Ramsey property if, whenever [\omega]2 is two-coloured, some monochromatic set is diverse with respect to at least one partition in the family. The authors show that no countable collection of even infinite partitions of \omega has the Ramsey property, but there always exists a collection of \aleph1 finite partitions of \omega with the Ramsey property.
Reviewer:  E.J.F.Primrose (Leicester)
Classif.:  * 05A18 Partitions of sets
Keywords:  diverse homogeneous sets; Ramsey property; partition

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