In set theory and in the context of a
large cardinal property
In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than the least Î ...
, 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
be the set of all finite subsets of ''D'' (see
Powerset#Subsets of limited cardinality) and let
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
. That is, ''f'' is constant on the unordered ''n''-tuples of elements of ''S''.
See also
*
Ramsey's theorem
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (say ...
*
Ramsey_cardinal In mathematics, a Ramsey cardinal is a certain kind of large cardinal number introduced by and named after Frank P. Ramsey, whose theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable case.
Let ...
{{settheory-stub
Large cardinals