I’m not sure if this is right, but I think that means that we will never prove Goldbach to be undecidable, since doing so would prove it was true and thereby contradict the claim that it is undecidable.
We could use one axiom system to prove that Goldbach is undecidable in Peano arithmetic. It would therefore be true.
We could use one axiom system to prove that Goldbach is undecidable in Peano arithmetic. It would therefore be true.