Omega is a description system for knowledge embedding which incorporates some of the attractive modes of expression in common sense reasoning such as descriptions, inheritance, quantification, negation, attributions and multiple viewpoints. A formalization of Omega is developed as a framework for investigations on the foundations of knowledge representation. As a logic, Omega achieves the goal of an intuitively sound and consistent theory of classes which permits unrestricted abstraction within a powerful logic system. Description abstraction is the construct provided in Omega corresponding to set abstraction. Attributions and inheritance are the basic mechanisms for knowledge structuring. To achieve flexibility and incrementality, the language allows descriptions with an arbitrary number of attributions, rather than predicates with a fixed number of arguments as in predicate logic. This requires a peculiar interpretation for instance descriptions, which in turn provides insights into the use and meaning of several kinds of attributions. The formal treatment consists in presenting semantic models for Omega, deriving an axiomatization and establishing the consistency and completeness of the logic.