This paper is an overview of results obtained by the author in the course of investigating the possible algebraic ways to extend elementary ordinary model theory of large models to include infinitary models, that is, those with relations of infinite rank . After describing briefly the algebraization of the basic notions of elementary ordinary model theory and stating the facts showing that no obvious generalization is possible, we define and characterize a class of algebras that we conjecture to be, in (...) some sense, the best proper algebraic generalization of the class of ordinary models in the given direction since it retains all the basic properties of the original one that meet some conditions similar to those of the Lindstrom theorem. (shrink)