 We now have a precise notion of a generalized quantifier, of which \(\forall\) and \(\exists\) are instances, along with infinitely many others. Moreover, we see how to extend first-order logic FO to a logic \(\FO(Q)\), by adding the clause  (5a)  to the formation rules, and the clause  (5b-i)  to the truth definition. Similarly if we add more than one generalized quantifier: \(\FO(Q_1,\ldots,Q_n)\).