Axiom of limitation of size
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In class theories, the axiom of limitation of size says that for any class C, C is a set (a class which can be an element of other classes) if and only if V (the class of all sets) cannot be mapped one-to-one into C.
This axiom is due to John von Neumann. It implies the axiom schema of specification, axiom schema of replacement, and axiom of global choice at one stroke. The axiom of limitation of size implies the axiom of global choice because the class of ordinals is not a set, so there is an injection from the universe to the ordinals. Thus the universe of sets is well-ordered.
[edit] See also
- Axiom of global choice
- Limitation of size
- Von Neumann–Bernays–Gödel set theory
- Morse–Kelley set theory
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