 Equational and quasi-equational classes of algebras  can be characterized by the closure properties they enjoy. A nonempty class of \(L\)-algebras is a variety if  it is closed under subalgebras, direct products, and homomorphic images. It is   a quasivariety   if it is closed under subalgebras, direct products, ultraproducts, isomorphic images, and contains a trivial algebra. It is easily seen that equational classes are varieties and that quasi-equational classes are quasiviarities. Birkhoff's theorem states that all varieties are equational classes and Malcev's theorem that all quasivarieties are quasi-equational classes. 