Varieties of Three-valued Heyting Algebras with a Quantifier

ABAD MANUEL; DíAZ VARELA JOSé PATRICIO; RUEDA LAURA

STUDIA LOGICA

Kluwer Academic Publishers.

Lugar: Netherlands.; Año: 2000 vol. 65 p. 181 - 198

0039-3215

This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q3 and we construct the lattice of subvarieties Ë(Q3) of the variety Q3.Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q3 and we construct the lattice of subvarieties Ë(Q3) of the variety Q3.Q3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q3 and we construct the lattice of subvarieties Ë(Q3) of the variety Q3.Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q3 and we construct the lattice of subvarieties Ë(Q3) of the variety Q3.Q3 and we construct the lattice of subvarieties Ë(Q3) of the variety Q3.