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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    Henryk Kotlarski (2004). The Incompleteness Theorems After 70 Years. Annals of Pure and Applied Logic 126 (1-3):125-138.
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