The schema of a database system consists of the constructs that model the entities of data. Schema evolution is the timely change of the schema and the consistent management of these changes. Dynamic schema evolution (DSE) is the management of schema changes while a database management system is in operation. DSE is a necessary facility of objectbase systems (OBSs) because of the volatile application domains that OBSs support. We propose a sound and complete axiomatic model for DSE in OBSs that supports the fundamental concepts of object-oriented computing such as subtyping and property inheritance. The model can infer all schema relationships from two identified input sets associated with each type called the essential supertypes and essential properties. These sets are typically specified by schema designers, but can be automatically supplied within an OBS. The inference mechanism performed by the model has a proven termination. The axiomatic model is a formal treatment of DSE in OBSs, which distinguishes it from other approaches that informally define a number of schema invariants and the rules that enforce them. An informal approach leads to multiple DSE mechanisms because of the differences in object models and the choices made by system designers. The lack of a common object model makes comparison of OBSs more difficult. The axiomatic model provides a solution for DSE in OBSs by serving as a common, formal underlying foundation for describing DSE of existing systems, which makes comparison of these systems much easier. A design space for OBSs based on the inclusion/exclusion of axioms is developed and can be used to classify, compare, and differentiate the features of OBSs. To test the expressibility of the model, the DSE of several OBSs are reduced to the axiomatic model and compared. Permission to make digital / hard copy of part or all of this work for personal or classroom use is granted without fee provided that the copies are not made or distributed for profit or commercial advantage, the copyright notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and / or a fee.