Ineffable cardinal

Ineffable cardinal

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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