 Axiom of global choice

A single class function chooses one member of every nonempty set. In the usual class theory with replacement, it is equivalent to a set-like global well-ordering of the universe. Ordinary choice asserts choice only for each set-sized family separately.

The Axiom of Global Choice is a concept in set theory, specifically in the context of the foundations of mathematics. It can be understood as a generalization of the Axiom of Choice. The Axiom of Choice states that given a collection of non-empty sets, it is possible to select exactly one element from each set, even if there is no explicit rule for making the selection.