Stronger Axioms
The axiom of constructibility and the generalized continuum hypothesis both imply the axiom of choice, but are strictly stronger than it.
In class theories such as Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, there is a possible axiom called the axiom of global choice which is stronger than the axiom of choice for sets because it also applies to proper classes. And the axiom of global choice follows from the axiom of limitation of size.
Read more about this topic: Axiom Of Choice
Famous quotes containing the words stronger and/or axioms:
“We cannot be any stronger in our foreign policy—for all the bombs and guns we may heap up in our arsenals—than we are in the spirit which rules inside the country. Foreign policy, like a river, cannot rise above its source.”
—Adlai Stevenson (1900–1965)
““I tell you the solemn truth that the doctrine of the Trinity is not so difficult to accept for a working proposition as any one of the axioms of physics.””
—Henry Brooks Adams (1838–1918)