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.
Famous quotes containing the words strong and/or cardinal:
“Women have their heads in their hearts. Man seems to have been destined for a superior being; as things are, I think women generally better creatures than men. They have weaker appetites and weaker intellects but much stronger affections. A man with a bad heart has been sometimes saved by a strong head; but a corrupt woman is lost forever.”
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