Abstract: Skyline query processing has recently received a lot of attention in database community. This is mainly due to the importance of skyline result in many applications, such as multi-criteria decision making, data mining and visualization, and user-preference queries. Presently, all the methods get the skyline set by directly executing query algebra operations on the original tables. However, these methods will not be applicable at all when the cardinality of the original tables and the number of dimensions become larger. Motivated by these facts, the query algebra operations on the skyline sets are first studied. The algebra operations only need the input of the skyline query processing to be the skyline sets whose size are much smaller than the original tables. A formalized model is also first proposed, which brings the set of multiple dimensional objects and the result set of skyline query together. And the instances of this formalized model can be used to study the query algebra operations on the skyline sets. Moreover, the cost model of the data model and query algebra operations is proposed. Extensive experiments demonstrate that the data model and query algebra operations are both efficient and effective.