Before we go on to Lindström's generalization, notice that any family of properties on dom("A") can be regarded as a monadic generalized quantifier. For example, the quantifier "there are exactly "n" things such that..." is a family of subsets of the domain of a structure, each of which has a cardinality of size "n". Then, "there are exactly 2 things such that φ" is true in A iff the set of things that are such that φ is a member of the set of all subsets of dom("A") of size 2.