 Recall that an SQML interpretation \(\calM\) for a first-order modal language \(\scrL_\Box\) specifies nonempty sets \(D\) and \(W\)—the “individuals” and “worlds” of \(\calM\)—along with a distinguished element \(w^\ast\) of \(W,\) the “actual” world of the interpretation; it then assigns a denotation \(\tau^\calM \in D\) to each term \(\tau\) and an extension \(\pi_w^\calM \subseteq D^n\) to each n-place predicate \(\pi\) at each world \(w\). A Kripke interpretation \(\calK\) of \(\scrL_\Box\) is exactly like an SQML interpretation except for one modification that reflects the fundamental actualist intuition noted above, viz., the addition of a function \(\textit{dom}\) that assigns to each world \(w\) of \(\calK\) a subset \(D_w\) of \(D\)—intuitively, of course, the individuals that exist in \(w\). No restrictions are placed on the domain of any world; any set of individuals, including the empty set, will do, although it is required that \(D = \bigcup\{\textit{dom}(w):w \in W\},\) i.e., that \(D\) consists of exactly the individuals that exist in some  world.[48]