Аннотация:
Part I proved that for every quasivariety K of structures
(which may have both operations and relations) there is a semilattice
S with operators such that the lattice of quasi-equational theories of
K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to
Con(S;+; 0; F). It is known that if S is a join semilattice with 0 (and no
operators), then there is a quasivariety Q such that the lattice of theories
of Q is isomorphic to Con(S;+; 0). We prove that if S is a semilattice
having both 0 and 1 with a group G of operators acting on S, and each
operator in G xes both 0 and 1, then there is a quasivariety W such
that the lattice of theories of W is isomorphic to Con(S;+; 0; G).