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 f is constant in finite subsets of S. More precisely, given a set D, let [math]\displaystyle{ \mathcal{P}_{\lt \omega}(D) }[/math] be the set of all finite subsets of D (see Powerset#Subsets of limited cardinality) and let [math]\displaystyle{ f: \mathcal{P}_{\lt \omega}(D) \to B }[/math] 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 [math]\displaystyle{ \mathcal{P}_{=n}(S) }[/math]. That is, f is constant on the unordered n-tuples of elements of S.Template:Needs citations

## See also

* Ramsey's theorem
* Ramsey cardinal

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