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

## See also

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