Well, the CH IS an example of a statement that is undecidable in ZF. Once you include is as an axiom, you essentially bypass the need to use ZF to justify it (o

Well, the CH IS an example of a statement that is undecidable in ZF. Once you include is as an axiom, you essentially bypass the need to use ZF to justify it (or prove it). So, just because you are able to include the CH as an axiom, doesn't mean it is not an example of a undecidable statement within a given set of axioms. Does that make sense?