 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", formula_1 (see Powerset#Subsets of limited cardinality) is the domain of "f" and for some element "r" of the range of "f", every member of formula_2 is mapped to "r".That is, "f" is constant on the unordered "n"-tuples of elements of "S".