I heard that, "ZFC theory doesn't allow self-reference."
But I don't know exactly what it means. As we can see in the proof of Godel's incompleteness theorem, we can use method of "Diagonalization" and we can make a self-reference sentence in ZFC.
It means,
P : a statement mentioning a statement whose Godel number is i
and by diagonalization technique, when P's Godel number is i, P can be a self-reference sentence.
What's the meaning of "ZFC theory doesn't allow self-reference."