A Short Guide to Gödel's Second Incompleteness Theorem

The usual proof of Godel's second incompleteness theorem for weak theories like I Sigma 'subscript 1' is long and technically cumbersome. The details are rarely given in full and in most cases they are skipped altogether with dismissing vague sentences alluding to the reader's ability to fill them in. In the first part of this note we provide a guide through the main technical points of the usual proof of Godel's theorem for weak theories. In the second part we present a different and simpler proof of the theorem for Zermelo-Fraenkel set theory, due to T. Jech, and we observe that it can be stretched to encompass weak theories, while avoiding many of the technicalities that are required in the usual proofs.