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:
“One strong wolf cannot defeat a pack of dogs; one strong arm cannot defeat many fists.”
—Chinese proverb.
“One must not make oneself cheap here—that is a cardinal point—or else one is done. Whoever is most impertinent has the best chance.”
—Wolfgang Amadeus Mozart (1756–1791)