A database over a schema is defined as a set of sets, one for each relation (in a relational database). The database corresponding to the source schema formula_3 would comprise the set of sets of tuples for each of the heterogeneous data sources and is called the "source database". Note that this single source database may actually represent a collection of disconnected databases. The database corresponding to the virtual mediated schema formula_2 is called the "global database". The global database must satisfy the mapping formula_4 with respect to the source database. The legality of this mapping depends on the nature of the correspondence between formula_2 and formula_3. Two popular ways to model this correspondence exist: "Global as View" or GAV and "Local as View" or LAV.