Geodesic
The interpolation problem in finite-layered pre-Heyting logics
Algebra i logika, Tome 58 (2019) no. 2, pp. 210-228.

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The interpolation problem over Johansson's minimal logic $\mathrm{ J}$ is considered. We introduce a series of Johansson algebras, which will be used to prove a number of necessary conditions for a $\mathrm{ J}$-logic to possess Craig's interpolation property $\mathrm{ (CIP)}$. As a consequence, we deduce that there exist only finitely many finite-layered pre-Heyting algebras with $\mathrm{ CIP}$.
Keywords: finite-layered pre-Heyting logic, Craig's interpolation property, Johansson algebra. 
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L. L. Maksimova; V. F. Yun. The interpolation problem in finite-layered pre-Heyting logics. Algebra i logika, Tome 58 (2019) no. 2, pp. 210-228. http://geodesic.mathdoc.fr/item/AL_2019_58_2_a4/

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