ABSTRACT
In Section 2.1 we introduced the concept of a hypersubstitution of type r, as a function
which assigns to every nt-ary operation symbol f x of the type an n^-ary term cr(/;). The application of hypersubstitutions to classes of algebras of type r , and to sets of equations of type r , led to a closure operator % defined both on sets of identities and on classes of algebras. Since \ is a closure operator, the corresponding systems of closed sets form complete lattices ([67]). In Section 2.2 varieties of type r which satisfy xW] — V were called solid. The set of all solid varieties of a given type r forms a sublattice S(r) of the lattice of all varieties of this type. We also proved that every solid variety is hyperequa tional, meaning that every solid variety is the class of hypermodels of a set of hyperidentities of type r.
