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:
“The weak are the most treacherous of us all. They come to the strong and drain them. They are bottomless. They are insatiable. They are always parched and always bitter. They are everyones concern and like vampires they suck our lifes blood.”
—Bette Davis (19081989)
“What people dont realize is that intimacy has its conventions as well as ordinary social intercourse. There are three cardinal rulesdont take somebody elses boyfriend unless youve been specifically invited to do so, dont take a drink without being asked, and keep a scrupulous accounting in financial matters.”
—W.H. (Wystan Hugh)