 This makes all necessarily equivalent propositions identical, for possible worlds can never disagree on them. “If Kennedy was shot, then Kennedy was shot” and “\(x^n + y^n = z^n\) has no integer solutions for \(n \gt 2\)” mean the same thing: the total set of worlds. This seems wrong, given that they don’t say the same thing: only one speaks about Diophantine equations. Similarly for necessary falsehoods: “Kennedy was both shot and not” and “\(2 + 3 = 6\)” are about different things, but they also end up expressing the same proposition: the empty set.