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

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Abad M., Cornejo J. M., Díaz Varela J. P.
Reports on Mathematical Logic
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2011
|
vol. 46
PL
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)* v (0 - 1)** = 11. 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.
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