On self-distributive weak Heyting algebras

Abstract

We use the left self-distributive axiom to introduce and study a special class of weak Heyting algebras, called self-distributive weak Heyting algebras (SDWH-algebras). We present some useful properties of SDWH-algebras and obtain some equivalent conditions of them. A characteristic of SDWH-algebras of orders 3 and 4 is given. Finally, we study the relation between the variety of SDWH-algebras and some of the known subvarieties of weak Heyting algebras such as the variety of Heyting algebras, the variety of basic algebras, the variety of subresiduated lattices, the variety of reflexive WH-algebras (RWH-algebras), and the variety of transitive WH-algebras (TWH-algebras).