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Projective Beth Property in Extensions of Grzegorczyk Logic

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Abstract

All extensions of the modal Grzegorczyk logic Grz possessing projective Beth's property PB2 are described. It is proved that there are exactly 13 logics over Grz with PB2. All of them are finitely axiomatizable and have the finite model property. It is shown that PB2 is strongly decidable over Grz, i.e. there is an algorithm which, for any finite system Rul of additional axiom schemes and rules of inference, decides if the calculus Grz+Rul has the projective Beth property.

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  1. Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Larisa Maksimova

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  1. Larisa Maksimova
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Correspondence to Larisa Maksimova.

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Dedicated to the memory of Willem Johannes Blok

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Maksimova, L. Projective Beth Property in Extensions of Grzegorczyk Logic. Stud Logica 83, 365–391 (2006). https://doi.org/10.1007/s11225-006-8309-1

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  • DOI: https://doi.org/10.1007/s11225-006-8309-1

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