Axiomatizability by sentences of the form (A)(E)! &p=q

CAMPERCHOLI, MIGUEL; VAGGIONE, DIEGO

Szeged, Hungria

Conferencia; Conference on Universal Algebra and Lattice Theorie; 2005

Bolyai Institute, University of Szeged

    Given an equational class V, several important subclasses of V can be defined by sentences of the form (A)(E)! &p=q. For example, if V is the class of all semigroups with unit, then the subclass of all groups can be defined in this way, and if V is the class of all bounded distributive lattices, then the subclass of  all Boolean lattices is also axiomatizable in this way. We consider the following general problem:    Problem: Given a variety V characterize the subclasses of V which can be axiomatized by a set of sentences of the form (A)(E)! &p=q.    We will present a solution to this problem for certain varieties of distributive lattice expansions.