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Varieties of Three-Valued Heyting Algebras with a Quantifier

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Abstract

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties Λ(Q 3 ) of the variety Q 3 .

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Abad, M., Díaz Varela, J., Rueda, L. et al. Varieties of Three-Valued Heyting Algebras with a Quantifier. Studia Logica 65, 181–198 (2000). https://doi.org/10.1023/A:1005211613539

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  • DOI: https://doi.org/10.1023/A:1005211613539

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