Given the number of results that are independent of ZF. It seems that once you've found a proof of a theorem that uses the axiom of choice, the odds are that it will be independent of ZF. So my ...
Is it possible to show that an infinite set has a countable (infinite) subset, without using the Axiom of Choice?
Let X be an infinite set. Is it possible to show the existence of a countably infinite subset of X without using the Axiom of Choice?
I recently saw the proof of the independence of ZF (with allowance for multiple empty sets) and AC. The proof constructed the model based on a set theory generated by infinitely many empty sets and ...