Chapter 4 develops the ultraproduct construction and proceeds to elaborate the theory of ultraproducts up to the natural embedding. It places particular emphasis on the construction of saturated models, since saturated universes have convenient properties that enable the proper development of the topological spaces required by nonstandard economics. After constructing nonstandard universes in full detail and proving that they possess the desired properties relevant to the development of nonstandard analysis, the chapter thoroughly explores the nature and existence of saturated models and proves the equivalence of saturation with the existence of concurrent or finitely satisfiable binary relations, as well as families of sets with the finite intersection property.