First-order definable counting-only queries

Many data sources can be represented easily by collections of sets of objects. For several practical queries on such collections of sets of objects, the answer does not depend on the precise composition of these sets, but only on the number of sets to which each object belongs. This is the case k= 1 for the more general situation where the query answer only depends on the number of sets to which each collection of at most k objects belongs. We …