Yes, Godel used Cantor's method of diagonalization in his proof. Turing also used it on the halting problem. Penrose talks about this in "The Emperor's New Mind

Yes, Godel used Cantor's method of diagonalization in his proof. Turing also used it on the halting problem. Penrose talks about this in "The Emperor's New Mind." Cantor rocked the Casbah. Smart people saw it and used it.