Existentially closed structures and Gödel's second incompleteness theorem

Publisher： Cambridge University Press

E-ISSN： 1943-5886|66|1|349-356

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.66, Iss.1, 2001-03, pp. : 349-356

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Abstract

We prove that any 1-closed (see def 1.1) model of the Π2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Gödel incompleteness theorem without the use of the Gödel diagonal lemma. We prove a few other theorems by the same method.

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