I agree with your logic but not your premise. Two alien species could effectively communicate if they happened to agree on a shared set of fundamental axioms. T

I agree with your logic but not your premise. Two alien species could effectively communicate if they happened to agree on a shared set of fundamental axioms. The axiom of choice is somewhat contentious here on earth, since it underlies the Banach-Tarski paradox, and it's not clear at all that a sophisticated alien society would have ever accepted the axiom of choice into their mathematics.