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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
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2694926
Page Count: 8
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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.
The Journal of Symbolic Logic © 2001 Association for Symbolic Logic