Abstract
A set H ⊆ ω is said to be diverse with respect to a partition Π of ω if at least two pieces of Π have an infinite intersection with H. A family of partitions of ω has the Ramsey property if, whenever [ ω] 2 is two-colored, some monochromatic set is diverse with respect to at least one partition in the family. We show that no countable collection of even infinite partitions of ω has the Ramsey property, but there always exists a collection of N 1 finite partitions of ω with the Ramsey property.
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