A Short Guide to Gödel's Second Incompleteness Theorem

Bagaria, Joan (2003) A Short Guide to Gödel's Second Incompleteness Theorem. Teorema, XXII (3). pp. 5-15.

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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.

Item Type: Article
Uncontrolled Keywords: K. Gödel; Incompleteness; Logic; Theory; weak
Subjects: Philosophie > Philosophische Journale, Kongresse, Vereinigungen > Teorema. Revista internacional de filosofia > Volume XXII (2003)
Philosophie > Philosophische Disziplinen > Logik, analytische Philosophie
Depositing User: Wolfgang Heuer
Date Deposited: 06 Dec 2020 13:45
Last Modified: 06 Dec 2020 13:46
URI: http://sammelpunkt.philo.at/id/eprint/2676

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