In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set.

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...) (Q 3 ) of the variety Q 3. (shrink)