On equivalences of database schemes

One of the fundamental questions in relation theory is the issue of equivalence between two database schemes. In [BMSU] two such schemes were defined to be equivalent when they have the same set of fixed points under the project-join maps associated with the two schemes. This definition requires in an explicit manner the existence of common universal relations, namely the joins, through which the two schemes exchange information, and the resulting “fiipoint” equivalence is a strong one: Both database schemes are in one-to-one correspondence with the subfamily of universal relations, the joins.