 For negative or neutral semantics, the extension at \(w\) of an \(n\)-place predicate \(P\) is a subset of \(\bD_w^n\). An atomic formula can be true at \(w\) only if all its singular terms have referents in \(\bD_w\); if not, it is false (in negative semantics) or truth-valueless (in neutral semantics). In a positive semantics, atomic formulas that are empty-termed at \(w\) may nevertheless be true at \(w\). Predicates are usually interpreted over the union \(\bU\) of domains of all the worlds, which functions as a kind of outer domain for each world, so that the extension of an \(n\)-place predicate \(P\) at a world \(w\) is a subset of \(\bU^n\). Some applications, however, require predicates to be true of—and singular terms to be capable of denoting—objects that exist in no world. If so, we may collect these objects into an outer domain that is a superset of \(\bU\). (They might be fictional objects, timeless Platonic objects, impossible objects, or the like.)