Existentially closed structures and gödel's second incompleteness theorem

Journal of Symbolic Logic 66 (1):349-356 (2001)
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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DOI 10.2307/2694926
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References found in this work BETA
A Note on Boolos' Proof of the Incompleteness Theorem.Makoto Kikuchi - 1994 - Mathematical Logic Quarterly 40 (4):528-532.
Kolmogorov Complexity and the Second Incompleteness Theorem.Makoto Kikuchi - 1997 - Archive for Mathematical Logic 36 (6):437-443.
Overspill and Fragments of Arithmetic.C. Dimitracopoulos - 1989 - Archive for Mathematical Logic 28 (3):173-179.
Other Proofs of Old Results.Henryk Kotlarski - 1998 - Mathematical Logic Quarterly 44 (4):474-480.

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Citations of this work BETA
Passive Induction and a Solution to a Paris–Wilkie Open Question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2):124-149.
The Incompleteness Theorems After 70 Years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.

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