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Existentially Closed Structures and Gödel's Second Incompleteness Theorem

Zofia Adamowicz and Teresa Bigorajska
The Journal of Symbolic Logic
Vol. 66, No. 1 (Mar., 2001), pp. 349-356
DOI: 10.2307/2694926
Stable URL: http://www.jstor.org/stable/2694926
Page Count: 8
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Existentially Closed Structures and Gödel's Second Incompleteness Theorem
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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 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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