ABSTRACT
Introduction. First order model theory can be viewed as the study of the class of elementary submodels of a large sufficiently saturated model M, as any (small) model of the first order theory of M embeds elementarily into M . In this sense, M can be used as a universal domain. To extend the methods of first order model theory to classes of models with more complicated axiomatisations, it becomes necessary to consider weaker notions of universal domains, as saturated models will in general not be in the class.
