 Where \(x\) is a fact, \(\ES(x)\) (the existence-set of \(x\)) is the set of all worlds at which \(x\) exists. And where \(G\) is a set of facts, \(\CES(G)\) (the conjunctive-existence-set of \(G\)) is \(\cap_{x\in G} \ES(x)\), i.e., the set of worlds at which all elements of \(G\) exist, and \(\DES(G)\) (the disjunctive-existence-set of \(G\)) is \(\cup_{x\in G} \ES(x)\), i.e., the set of worlds at which some elements of \(G\) exist. Notice that \(\CES(\varnothing) = W\), \(\DES(\varnothing) = \varnothing\), and that given any \(G \ne \varnothing\), \(\CES(G) \subseteq \DES(G)\). (Here and elsewhere, we borrow some vocabulary and symbolism from Fine 1982.)