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In set theory and in the context of a large cardinal property, a subset, S, of D is homogeneous for a function f if f is constant in finite subsets of S. More precisely, given a set D, let P < ω {\displaystyle {\mathcal {P}}_{<\omega }} be the set of all finite subsets of D and let f : P < ω → B {\displaystyle f:{\mathcal {P}}_{<\omega }\to B} be a function defined in this set. On these conditions, S is homogeneous for f if, for every natural number n, f is constant in the set P = n {\displaystyle {\mathcal {P}}_{=n}}. That is, f is constant on the unordered n-tuples of elements of S.