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Existentially closed structures and Gödel's second incompleteness theorem

Published online by Cambridge University Press:  12 March 2014

Zofia Adamowicz  and
Teresa Bigorajska
Zofia Adamowicz
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, Šniadeckich 8, 00-950 Warszawa, Poland, E-mail: zosiaa@impan.gov.pl
Teresa Bigorajska
Affiliation:
Faculty of Mathematics, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warszawa, Poland, E-mail: teresabi@impan.gov.pl
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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 Gödel incompleteness theorem without the use of the Gödel diagonal lemma. We prove a few other theorems by the same method.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 349 - 356
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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