The Variety of Semi-Heyting Algebras Satisfying the equation (0 → 1)* v (0 → 1)** ≈ 1

In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity (0  1)  (0  1)  1. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We also determine the sublattice generated by the subvarieties introduced in [4, Definition 8.1] within the lattice of subvarieties of semi-Heyting algebras REPORTS ON MATHEMATICAL LOGIC 46 (2011), 75–90 Manuel ABAD, Juan Manuel CORNEJO and José Patricio DÍAZ VARELA THE VARIETY OF SEMI-HEYTING ALGEBRAS SATISFYING THE EQUATION (0 → 1) ∨ (0 → 1) ≈ 1 A b s t r a c t. In [4, Definition 8.1], some important subvarieties of the variety SH of semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety ISSH of SH, characterized by the identity (0 → 1) ∨ (0 → 1) ≈ 1. We prove that ISSH contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of SH with this property. We also determine the sublattice generated by the subvarieties introduced in [4, Definition 8.1] within the lattice of subvarieties of semi-Heyting algebras. I wish to dedicate this work to my father Francisco Cornejo. The support of CONICET is grateful acknowledged Received 10 September 2009 Publikacja objęta jest prawem autorskim. Wszelkie prawa zastrzeżone. Kopiowanie i rozpowszechnianie zabronione 76 MANUEL ABAD, JUAN MANUEL CORNEJO AND JOSÉ PATRICIO DÍAZ VARELA .