Mathematical interpretation of formal systems

More than 30 years ago I proved by use of a theorem of Lowenheim that a theory based on axioms formulated in the lower predicate calculus could always be satisfied in a denumerable infinite domain of objects. Later one has often expressed this by saying that a denumerable model exists for such a theory. Of particular interest was of course the application of this theorem to axiomatic set theory, showing that also for this an arithmetical model can be found. As I emphasized this leads to a relativisation of set theoretic notions.