Ineffable cardinal
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In mathematics, an ineffable cardinal is a certain kind of large cardinal number.
Formally, a cardinal number κ is ineffable if and only if 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) if and only if 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.
References:
Harvey Friedman: "Subtle Cardinals and Linear Orderings." Annals of Pure and Applied Logic (January 15, 2001) 107(1-3):1-34.
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