Abstract. The Meta Object Facility (MOF) 2.0 and the Unified Modeling Language Infrastructure introduce new language features such as subsets, (derived) unions and redefinitions, but without a precise semantics. This is a problem since they are used throughout the definition of the Unified Modeling Language (UML) 2.0. We give our understanding of these new language features by formalizing the structural constraints imposed by subsets and unions on metamodels and models using Liskov substitutability as the main criterion. We expect that this article provides a better understanding of the foundations of the MOF 2.0, which is necessary to define model transformation languages and tools.