 Both approaches take place in a singular metalanguage. Since the models are based on set theory, they require the domain of individuals to form a set. Furthermore, the definition of satisfaction explains what is for a formula \(\forall xx A\) to be satisfied in a model by an assignment in terms of singular quantification over non-empty subsets of the domain of individuals. This may perhaps encourage the impression that plural quantification is only intelligible as singular quantification over non-empty sets of individuals. Note, however, that neither the use of set-based models nor the use of singular quantification in the definition of satisfaction for a formula of the form \(\forall xx\) is compulsory. In a plural metatheory in which we have a theory of ordered pairs, one may adapt the generalized conception of an interpretation developed in Rayo &amp; Uzquiano (1999) to provide a plural model theory in which one uses neither. This model theory is developed, for example, in Burgess 2004.