Existentially closed structures and gödel's second incompleteness theorem
Journal of Symbolic Logic 66 (1):349-356 (2001)
| Abstract | We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method | |||||||||
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Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
Carlo Cellucci (1992). Gödel's Incompleteness Theorem and the Philosophy of Open Systems. In Daniel Miéville (ed.), Kurt Gödel: Actes du Colloque, Neuchâtel 13-14 Juin 1991, pp. 103-127. Travaux de logique N. 7, Université de Neuchâtel.
Yi-Zhuang Chen (2004). Edgar Morin's Paradigm of Complexity and Gödel's Incompleteness Theorem. World Futures 60 (5 & 6):421 – 431.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
Carlo Cellucci (1993). From Closed to Open Systems. In J. Czermak (ed.), Philosophy of Mathematics, pp. 206-220. Hölder-Pichler-Tempsky.
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