In this paper we prove that the free algebras in a subvariety equation image of the variety equation image of semi-Heyting algebras are directly decomposable if and only if equation image satisfies the Stone identity.

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

ABSTRACT The variety O2 of double Ockham algebras consists of the algebras of type where and are Ockham algebras. In [16], M. Sequeira introduced several subvarieties of O2. In this paper we give a construction of free double Ockham algebras on a partially ordered set. We also describe free objects for the subvarieties of O2 considered in [16].

In this work we provide a new topological representation for implication algebras in such a way that its one-point compactification is the topological space given in [1]. Some applications are given thereof.