The Variety of Semi-Heyting Algebras Satisfying the equation $(0 \to 1)^* \vee (0 \to 1)^{**} \approx 1$

MANUEL ABAD; JUAN MANUEL CORNEJO; JOSÉ PATRICIO DÍAZ VARELA

Reports on Mathematical Logic

Jagiellonian University Press

Año: 2011 vol. 46 p. 75 - 90

0137-2904

In cite[Definition 8.1]{SanSH}, some important subvarieties of the variety $mathcal{SH}$ of Semi-Heyting algebras are defined. The purpose of this paper is to introduce and investigate the subvariety $mathcal{ISSH}$ of $mathcal{SH}$, characterized by the identity $(0 o 1)^{*} ee (0 o 1)^{**} approx 1$. We prove that $mathcal{ISSH} $ contains all the subvarieties introduced by Sankappanavar and it is in fact the least subvariety of $mathcal{SH}$ with this property. We also determine the sublattice generated by the subvarieties introduced in cite[Definition 8.1]{SanSH} within the lattice of subvarieties of semi-Heyting algebras.