Existentially closed structures and gödel's second incompleteness theorem

Journal of Symbolic Logic 66 (1):349-356 (2001)
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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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Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
The Incompleteness Theorems After 70 Years.Henryk Kotlarski - 2004 - Annals of Pure and Applied Logic 126 (1-3):125-138.
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 Scope of Gödel’s First Incompleteness Theorem.Bernd Buldt - 2014 - Logica Universalis 8 (3-4):499-552.

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References found in this work

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.
Other Proofs of Old Results.Henryk Kotlarski - 1998 - Mathematical Logic Quarterly 44 (4):474-480.
Overspill and Fragments of Arithmetic.C. Dimitracopoulos - 1989 - Archive for Mathematical Logic 28 (3):173-179.

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