 We distinguish quantifier expressions from what they signify or denote, the (generalized) quantifiers themselves. In logical languages, quantifier expressions are variable-binding operators. Thus, \(\exists\) is the familiar operator such that in a formula \(\exists  x\f\),[2]  \(\exists x\) binds all free occurrences of x in \(\f\). It signifies the quantifier “there exists”—we’ll see shortly exactly what this object is. Likewise, the symbol \(Q_0\) is often used as a variable-binding operator signifying “there exist infinitely many”.