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**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 \aleph_{1} 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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