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Object-oriented and object-relational DBMS support set valued attributes, which are a natural and concise way to model complex information. However, there has been limited research to-date on the evaluation of query operators that apply on sets. In this paper we study the join of two relations on their set-valued attributes. Various join types are considered, namely the set containment, set equality, and set overlap joins. We show that the inverted file, a powerful index for selection queries, can also facilitate the efficient evaluation of most join predicates. We propose join algorithms that utilize inverted files and compare them with signature-based methods for several set-comparison predicates.