 Say that a set of facts \(G\) is independent iff \(G\) is not empty and any of its subsets \(H\) is such that there is a domain \(F_w\) such that such that \(G \cap F_w = H\). That \(G\) is independent means (i) that any collection of facts in \(G\) may obtain together without any other fact in \(G\) obtaining, and (ii) that no fact in \(G\) need obtain.