The Closed Fragment of the Interpretability Logic of PRA with a Constant for $\mathrm{I}\Sigma_1$

Notre Dame Journal of Formal Logic 46 (2):127-146 (2005)
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Abstract

In this paper we carry out a comparative study of $\mathrm{I}\Sigma_1$ and PRA. We will in a sense fully determine what these theories have to say about each other in terms of provability and interpretability. Our study will result in two arithmetically complete modal logics with simple universal models

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10.1305/ndjfl/1117755145

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Joost Joosten
Universitat de Barcelona

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References found in this work

Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.
Arithmetization of Metamathematics in a General Setting.Solomon Feferman - 1960 - Journal of Symbolic Logic 31 (2):269-270.
The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
On n-quantifier induction.Charles Parsons - 1972 - Journal of Symbolic Logic 37 (3):466-482.

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