## Journal of Symbolic Logic

### Existentially Closed Structures and Godel's Second Incompleteness Theorem

#### Abstract

We prove that any 1-closed (see def 1.1) model of the $\Pi_2$ consequences of PA satisfies $\neg$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.

#### Article information

Source
J. Symbolic Logic, Volume 66, Issue 1 (2001), 349-356.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746375

Mathematical Reviews number (MathSciNet)
MR1825189

Zentralblatt MATH identifier
0981.03043

JSTOR