 Like in the case of second-order logic, we may provide at least two sorts of models for the theory of plural quantification. In both cases, we interpret plural quantification in terms of quantification over non-empty sets of individuals in the domain \(D\). The difference is that in standard models we let plural variables range over the full power set of \(D\), whereas plural variables range over a set \(S\) of non-empty subsets of \(D\), provided only that \(S\) contains all sets definable by some formula.