Axiom of global choice
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In class theories, the axiom of global choice is a stronger variant of the axiom of choice which applies to proper classes as well as sets. It can be expressed in various ways which are only apparently different.
"Weak" form: Every class of nonempty sets has a choice function.
"Strong" form: Every collection of nonempty classes has a choice function. (Restrict the possible choices in each class to the subclass of sets of minimal rank in the class. This subclass is a set. The collection of such sets is a class.)
V \ { ∅ } has a choice function (where V is the class of all sets).
There is a well-ordering of V.
In Gödel-Bernays, global choice does not add any consequence about sets beyond what could have been deduced from the ordinary axiom of choice.
[edit] See also
- Axiom of choice
- Axiom of limitation of size
- Von Neumann–Bernays–Gödel set theory
- Morse–Kelley set theory
[edit] References
- Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. ISBN 3-540-44085-2.
- John L. Kelley; General Topology; ISBN 0-387-90125-6
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