Strong partition cardinal

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In Zermelo-Fraenkel set theory without the axiom of choice a strong partition cardinal is an uncountable well-ordered cardinal such that every partition of the set of size subsets of into less than pieces has a homogeneous set of size .

The existence of strong partition cardinals contradicts the axiom of choice. The Axiom of determinacy implies that ℵ1 is a strong partition cardinal.

References

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