Virtual algebraic isomorphisms between predicate calculi of finite rich signatures

It is proved that every two predicate calculi of finite rich signatures are algebraically virtually isomorphic, i.e., some of their Cartesian extensions are algebraically isomorphic. As an important application, it is stated that for predicate calculi in any two finite rich signatures, there exists a computable isomorphism between their Tarski–Lindenbaum algebras which preserves all model-theoretic properties of an algebraic type corresponding to the real practice of research in model theory.