3 ms·
Firstly, the sentence you quoted, while unfortunately ambiguous, is correct if you take "of which" as picking up "assumptions" instead of "results". That is, t
by waqf 10y ago
Firstly, the sentence you quoted, while unfortunately ambiguous, is correct if you take "of which" as picking up "assumptions" instead of "results". That is, the assumptions, of which a famous one is AC, have counterintuitive consequences, of which the original poster does not give an example but Banach–Tarski is a commonly cited one.
Secondly, the axiom of choice may be independent of ZF (depending on whether ZF is consistent) but it is certainly not independent of ZFC :).
- justinpombrio 10y ago> Firstly, the sentence you quoted, while unfortunately ambiguous, is correct if you take "of which" as picking up "assumptions" instead of "results". Oh, that's what Koshkin was trying to say. > Secondly, the axiom of choice is not independent of ZFC, it's independent of ZF (assuming ZF is consistent) :). Ah, the C stands for choice...