Equational bases for three-valued Heyting algebras with a quantifier

ABAD, MANUEL; DÍAZ VARELA, JOSÉ PATRICIO; RUEDA, LAURA; SUARDIAZ ANA

Bahía Blanca

Congreso; V Congreso Dr. Antonio Monteiro; 1999

An equational basis is given for some members of the lattice of subvarieties of three-valued Q-Heyting algebras. For any finite subdirectly irreducible algebra A, an equation which describes the number of order-connected components (o.c.c.´s) of the set J = J(A) of join-irreducible elements of A is provided. Then an equation is exhibited characterizing the number of elements of Max(J)Min(J). Finally an inductive process is shown to determine the number of maximal non minimal elements in each o.c.c. of J.