European summer meeting of the Association for Symbolic Logic
László Csirmaz · Journal of Symbolic Logic · 1993
Call the variety of algebras V congruence distributive if the lattice of cong of V is distributive.The following theorem gives an answer to problem (2) fo tributive varieties.THEOREM.Let V be a congruence distributive variety generated by its finite m every member of V has a one-element subalgebra.Then if Amal( V) is an elemen under reduced products.Thus, in that case Amal(V) is determined by Horn sente EXAMPLE AND COUNTEREXAMPLE.It is well known that a lattice L is modula pentagon N as its sublattice (N is a five-element lattice generated by x, y, an is noncomparable with x and y).It is shown by Bergman that if V is a latti finite modular lattice, then Amal(V) is not elementary, which gives a negativ On the other hand, if V is generated by N, then Amal(V) is an elementary sentences.