Corpus ID: 237491961

# Provability Logic: models within models in Peano Arithmetic

```@inproceedings{Berarducci2021ProvabilityLM,
title={Provability Logic: models within models in Peano Arithmetic},
author={Alessandro Berarducci and Marcello Mamino},
year={2021}
}```
• Published 12 September 2021
• Mathematics
In 1994 Jech gave a model-theoretic proof of Gödel’s second incompleteness theorem for Zermelo-Fraenkel set theory in the following form: ZF does not prove that ZF has a model. Kotlarski showed that Jech’s proof can be adapted to Peano Arithmetic with the role of models being taken by complete consistent extensions. In this note we take another step in the direction of replacing proof-theoretic by model-theoretic arguments. We show, without passing through the arithmetized completeness theorem… Expand

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