What are the things that “break” if the axiom of choice is false? I’ve been wondering if the axiom of choice has some relationship to an argument for the exis

What are the things that “break” if the axiom of choice is false? I’ve been wondering if the axiom of choice has some relationship to an argument for the existence of free will. Not just because they share a name, but because you can think of physics as being a multiplayer game.