# Homogeneous (large cardinal property)

In set theory and in the context of a large cardinal property, a subset, S, of D is homogeneous for a function f if for some natural number n, ${\displaystyle {\mathcal {P}}_{=n}(D)}$ (see Powerset#Subsets of limited cardinality) is the domain of f and for some element r of the range of f, every member of ${\displaystyle {\mathcal {P}}_{=n}(S)}$ is mapped to r. That is, f is constant on the unordered n-tuples of elements of S.