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arXiv · 2604.02082

Fischer-Servi logic does not have interpolation

Rodrigo Nicolau Almeida·Nick Bezhanishvili·Simon Lemal
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Abstract

We prove that the Fischer-Servi logic $\mathsf{IK}$ does not have the (Craig) interpolation property. This is obtained by showing that the corresponding class of modal Heyting algebras lacks the amalgamation property. We also generalize this result to some extensions of the Fischer-Servi logic such as $\mathsf{IT}$, $\mathsf{IK4}$, $\mathsf{IS4}$, and $\mathsf{IGL}$.

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Rodrigo Nicolau Almeida, Nick Bezhanishvili, Simon Lemal. 2026-04-02. Fischer-Servi logic does not have interpolation. https://arxiv.org/abs/2604.02082

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