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Reports on Mathematical Logic

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No. 29 (1995)

Katarzyna IDZIAK

QUASIVARIETES OF EQUIVALENTIAL ALGEBRAS
A b s t r a c t.
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.

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