 Where \(w\) is a world, let \(P_w\) be the set of propositions which exists in it, and let \(P\) be \(\cup_{w\in W} P_{w}\), the set of all propositions. On the view that to be a fact is to be a true proposition, the set of facts which exist in world \(w\) is the set of all propositions which exist and are true at \(w\), i.e., \(F_{w} = T_w \cap P_{w}\), and the existence-set of a fact \(x\) is \(\ES(x) \cap \TS(x)\). (There is a similar view according to which all facts are true propositions, while some true propositions—say, the complex ones—may not be facts, but we leave it aside.) Of course, under the assumption that no proposition can be true without existing, in particular under the assumption that they exist necessarily, for every world \(w, F_{w} = T_{w}\), and the existence-set of a fact \(x\) is \(\TS(x)\).