Non-finite specifiability of projections of functional dependency families (Q1082095)

A functional dependency (FD) (implicational dependency (ID)) family is a family of relational database instances consisting of all instances which satisfy a given set of FDs (IDs). An ID family is finitely specifiable if it can be defined using a finite set of IDs. It is known that all FD families are finitely specifiable ID families, and also that each projection of each FD family, while not necessarily an FD family, is an ID family. It is shown here that if the projection of an FD family is not an FD family, then it is not a finitely specifiable ID family.