There's another paper called "Incompleteness Ex Machina" with several proofs of both the first and second incompleteness theorems. https://arxiv.org/abs/1909.0

There's another paper called "Incompleteness Ex Machina" with several proofs of both the first and second incompleteness theorems. https://arxiv.org/abs/1909.04569 https://arxiv.org/abs/1909.04569