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. In mathematics, the axiom of choice, or AC, is an axiom of set theory. ...
"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).
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