Ineffably Ramsey cardinal
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In mathematics, an ineffably Ramsey cardinal (named after Frank P. Ramsey and after ineffable cardinals) is a certain kind of large cardinal number.
Formally, a cardinal number κ such that for every function f:[ κ] < ω → {0, 1} (with [κ] < ω denoting the set of all finite subsets of κ) there is a stationary set A that is homogeneous for f (i.e.: for every n, f is constant on the n-tuples from A) is called Ramsey.
It is obvious from the definition that an ineffably Ramsey cardinal is both Ramsey and totally ineffable.
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