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:
“And when a woman’s will is as strong as the man’s who wants to govern her, half her strength must be concealment.”
—George Eliot [Mary Ann (or Marian)
“The Poles do not know how to hate, thank God.”
—Stefan, Cardinal Wyszynski (1901–1981)