A model for a two-sorted language, for example, may consist of an ordered triple $\langle D_1 , D_2 I\rangle$ in which $D_1 $and $D_2 $specify the domain of quantification associated to each style of variable, and $I$ is an interpretation function, which assigns appropriate values and extensions to each expression in the non-logical vocabulary.
Other predicates may nevertheless take arguments of different sorts; for example, in a two-sorted language in which lowercase variables range over numbers and uppercase variables range over sets of numbers, $x \epsilon X$, for example, can take as arguments variables of different sorts and may be read "$x$ is in $X$".
For each many-sorted language with $n$ styles of variable, we may introduce a one-sorted language, which comes with a one-place predicate, $S_i$, for each sort in the many-sorted language.
In a many-sorted language with functional symbols and individual constants, each singular term would be assigned a single sort.
We may, in addition, turn each model for the many-sorted language $\langle D_1,, \ldots, D_n, I \rangle$ into a model for the resulting one-sorted language $\langle \bigcup_{n} D_n, I^\ast \rangle$ in which we take the domain to consist in the union of the domains associated to each original sort.
A many-sorted language is expressively equivalent to a single sorted one which has additional predicates for the various sorts of things.
However, the move to a many-sorted language is largely a matter of convenience.
Formulæ of the one-sorted language obtained in this way from formulæ of type theory are said to be stratified.
Quine's move in [1937a] is the natural one of taking the pseudoformulæ like (A) and thinking of them as genuine formulæ in a new, one-sorted, language.
Take language, for example.
Use figurative language for effect.
