Page "Axiom of choice" Paragraph 78

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC ( ZF plus AC ).

Equivalently, these statements are true in all models of ZFC but false in some models of ZF.