M-solid Quasivarieties

Abstract

Solid quasivarieties were first mentioned in [5] and generalized in [1] to M-solid quasivarieties. In this paper we develop the theory of M-solid quasivarieties on the basis of two Galois-connections and a pair of additive closure operators. Using a different definition of an M-hyperquasiidentity we define weakly M-solid quasivarieties and show that they form a complete sublattice of the lattice of all quasivarieties of a given type. The complete lattice of all M-solid quasivarieties is a complete sublattice of the complete lattice of all weakly M-solid quasivarieties of the same type.