Almost ineffable cardinal
- Almost ineffable cardinal
In mathematics, an almost ineffable cardinal is a certain kind of large cardinal number.
Formally, a cardinal number κ is almost ineffable if and only if for every f: κ → P(κ) with the property that f(δ) is a subset of δ for all ordinals δ, there is a subset S of κ having cardinal κ and homogeneous for f, in the sense that for any δ1 < δ2 in S, f(δ1) = f(δ2) intersect δ1.
If the homogeneous subset is also stationary in κ, the cardinal is ineffable.
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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