Ineffable cardinal
In
mathematics, a
cardinal number &kappa is an
ineffable cardinal iff for every f: κ
2 → {0, 1), there is a stationary subset of κ that is
homogeneous for f. κ is n-ineffable (for a positive integer n) iff for every f: κ
n → {0, 1), there is a stationary subset of κ that is homogeneous for f. A totally ineffable cardinal is a cardinal that is n-ineffable for every n. If κ is n+1-ineffable, then the set of n-ineffable cardinals below κ is a stationary subset of κ.