Abstract

The expressive power of constants in the quasiequational logic is considered. We describe three 3 element algebras $A_1, A_2, A_3$ such that $A_{i+1}$ is obtained from $A_i$ by adding one constant to the signature and such that the quasivariety generated by $A_2$ has infinitely many subquasivarieties while both $A_1$ and $A_3$ generate quasivarieties with finitely many subquasivarieties. Moreover, each of the $A_i$'s generates a congruence permutable variety.