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- W4286979908 abstract "In 1994 Jech gave a model theoretic proof of Godel'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, that the existence of a model of PA of complexity $Sigma^0_2$ is independent of PA, where a model is identified with the set of formulas with parameters which hold in the model. Our approach is based on a new interpretation of the provability logic of Peano Arithmetic with the modal operator interpreted as truth in every $Sigma^0_2$-model." @default.
- W4286979908 created "2022-07-25" @default.
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- W4286979908 date "2021-09-12" @default.
- W4286979908 modified "2023-09-26" @default.
- W4286979908 title "Provability Logic: models within models in Peano Arithmetic" @default.
- W4286979908 doi "https://doi.org/10.48550/arxiv.2109.05476" @default.
- W4286979908 hasPublicationYear "2021" @default.
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