Abstract
Given a function f a subset of its domain is a rainbow subset for f if f is one to one on it. We start with an old Erd˝os Problem: Assume f is a coloring of the pairs of !1 with three colors such that every subset A of !1 of size !1 contains a pair of each color. Does there exist a rainbow triangle ? We investigate rainbow problems and results of this style for colorings of pairs establishing negative “square bracket” relations.
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