A family of simple models for database systems is defined, where a system is composed of a scheduler, a data manager and several user transactions. The basic correctness criterion for such systems is taken to be consistency preservation. The central notion of the paper is that of a general purpose scheduler, a database system scheduler that is blind to the semantics of transactions and integrity assertions. Consistency preservation of a database system is shown to be precisely equivalent to a restriction on the output of a general purpose scheduler GPS, called weak serializability. That is, any database system using GPS will preserve consistency iff the output of GPS is always weakly serializable. This establishes a tight connection between database system correctness and scheduler behavior. Also, aspects of restart facilities and predeclared data accesses are discussed. Finally, several examples of schedulers correct with respect to weak serializability are presented.