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:
“Say never the strong heart
In the consuming breath
Cries out unto the dark
The skinny death.”
—Allen Tate (1899–1979)
“Time and I against any two.”
—Spanish proverb.
Quoted by Cardinal Mazarin during the minority of Louis XIV.