Varieties of Three-Valued Heyting Algebras with a Quantifier |
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| Authors: | Abad M Díaz Varela JP Rueda LA Suardíaz AM |
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| Institution: | (1) Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina;(2) Departamento de Matemática, Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina |
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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  (Q
3
) of the variety Q
3
. |
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| Keywords: | quantifiers Heyting algebras distributive lattices varieties equational bases |
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