A Simple Proof of Arithmetical Completeness for -Conservativity Logic

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

Giorgi Japaridze

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

Abstract

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.

Primary Subjects: 03B45

Secondary Subjects: 03F30, 03F40

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040511342
Mathematical Reviews number (MathSciNet): MR1326118
Digital Object Identifier: doi:10.1305/ndjfl/1040511342
Zentralblatt MATH identifier: 0822.03013

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