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Varieties of Three-Valued Heyting Algebras with a Quantifier

M. Abad, J. P. Díaz Varela, L. A. Rueda and A. M. Suardíaz
Studia Logica: An International Journal for Symbolic Logic
Vol. 65, No. 2 (Jul., 2000), pp. 181-198
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016176
Page Count: 18
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Abstract

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

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