The Expressive Power of Cardinality-Bounded Set Values in Object-Based Data Models

In object based data models complex values such as tuples or sets have no special status and are represented just as any other object However di erent objects may represent the same value i e dupli cates may occur It is known that typical object based models sup porting rst order queries standard object creation and while loops cannot in general guarantee the duplicate freeness of representations of set values In this paper we consider a number of extensions of the basic object based model which provide exactly this ability under the assumption that a xed bound is known on the cardinality of the set values We show that these extensions are all equivalent to each other Our main result is that increasing the cardinality bound from m to m yields strictly more expressive extensions except for m and m We thus establish a non collapsing hierarchy Extended and revised version of a paper presented at the Fourth International Con ference on Database Theory Research Assistant of the NFWO Address Dept Math Computer Sci Uni versity of Antwerp UIA Universiteitsplein B Antwerp Belgium E mail vdbuss wins uia ac be Computer Science Department Indiana University Bloomington IN USA E mail vgucht cs indiana edu