axiom of choice
p
basic constructions:
strong axioms
further
The axiom of choice is the following statement:
This means: for every surjection of sets, there is a function (a section), such that
Note that a surjection of sets can be regarded as a -indexed family of inhabited sets, while the existence of a section is equivalent to a choice of one element in each set of this family. This reproduces the more classical form of the axiom of choice.
When the full axiom of choice fails, it may still be valid for some...