This paper presents part of a formalism proposal using set theory for a reference object model, being developed as a doctoral research thesis at the School of Electrical and Computer Engineering of the State University of Campinas (Unicamp), Brazil. The proposed reference object model is compatible to the standard ODMG-93, however more generic. The formalism uses set theory concepts to define types, classes, encapsulation, subtyping, inclusion and overloading polymorphism, instances (object/values), object identity and types/classes extents (extensions). The set theory concepts used are domains, relations (domain mappings), domain-relation associations, set inclusion and functional inclusion. This paper will only present the formalism related to abstract concepts of an object model, e.g. types, classes encapsulation, subtyping and polymorphism. The main contribution of this work is a step toward a mathematical foundation for standardization efforts of object models for Object Oriented Database Systems.