For me the easiest way to prove Gödel first's with perfect rigor, without bothering with numberings (but using computational undecidability) is here http://users.utu.fi/jkari/automata/fullnotes.pdf (Section 4.10)
For me the easiest way to prove Gödel first's with perfect rigor, without bothering with numberings (but using computational undecidability) is here http://users.utu.fi/jkari/automata/fullnotes.pdf (Section 4.10)