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:
“You thought you could be Mrs. de Winter. Live in her house. Walk in her steps. Take the things that were hers. But she’s too strong for you. You can’t fight her. No one ever got the better of her. Never. Never. She was beaten in the end. But it wasn’t a man. It wasn’t a woman. It was the sea!”
—Robert E. Sherwood (1896–1955)
“Time and I against any two.”
—Spanish proverb.
Quoted by Cardinal Mazarin during the minority of Louis XIV.