> First, the axiom of voice requires that you have a countable number of sets that you are choosing elements from, but there are undoubtably many of the equival

> First, the axiom of voice requires that you have a countable number of sets that you are choosing elements from, but there are undoubtably many of the equivalence classes that he described [0]. No it does not? The axiom of countable choice [0] is a strictly weaker axiom. [0] https://en.wikipedia.org/wiki/Axiom_of_countable_choice https://en.wikipedia.org/wiki/Axiom_of_countable_choice