Abstract

In the classes of algebra such as lattices, groups and ring there are nite algebras, each generating not nitely axiomatizable quasivariety. We indi- cate here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, the lattice join of two nitely axiomatizable quasivarieties, each generated by a nite Heyting or topo- logical Boolean algebra, respectively, need not be nitely axiomatizable. Finally, we solve problem 4 asked in Rautenberg [2].