Notre Dame Journal of Formal Logic

A Simple Proof of Arithmetical Completeness for $\Pi_1$-Conservativity Logic

Giorgi Japaridze


Hájek and Montagna proved that the modal propositional logic ILM is the logic of $\Pi_1$-conservativity over sound theories containing I$\Sigma_1$ (PA with induction restricted to $\Sigma_1$ formulas). I give a simpler proof of the same fact.

Article information

Notre Dame J. Formal Logic, Volume 35, Number 3 (1994), 346-354.

First available in Project Euclid: 21 December 2002

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Zentralblatt MATH identifier

Primary: 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45}
Secondary: 03F30: First-order arithmetic and fragments 03F40: Gödel numberings and issues of incompleteness


Japaridze, Giorgi. A Simple Proof of Arithmetical Completeness for $\Pi_1$-Conservativity Logic. Notre Dame J. Formal Logic 35 (1994), no. 3, 346--354. doi:10.1305/ndjfl/1040511342.

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