Linear Heyting algebras with a quantifier Original Research Article

A Q-Heyting algebra is an algebra (H;∨,∧,→,∇,0,1) of type (2,2,2,1,0,0) such that (H;∨,∧,→,0,1) is a Heyting algebra and the unary operation ∇ satisfies the conditions ∇0=0, a∧∇a=a, ∇(a∧∇b)=∇a∧∇b and ∇(a∨b)=∇a∨∇b, for any a, b∈H. This paper is devoted to the study of the subvariety View the MathML source of linear Q-Heyting algebras. Using Priestley duality we investigate the subdirectly irreducible linear Q-Heyting algebras and, as consequences, we derive some properties of the lattice of subvarieties of View the MathML source and find equational bases for some of these subvarieties.