The number of keys in relational and nested relational databases

Combinatorial propositions, concerning the maximal number of minimal keys are considered. It is shown that the results of Demetrovics about the maximal number of minimal keys on unbounded domains do not hold for finite domains. Using this result lower bounds for the size of minimum-sized Armstrong relations are derived. It is also shown that the maximal number of minimal keys in databases on nonuniform domains is also precisely exponential in the number of attributes like in the case of uniform domains. In relational database theory and practice, it is often postulated that none of the attributes of the primary key may ever obtain