Some theorems on the expressive limitations of modal languages (Q792997)

Certain interesting conditions on S5-modal models which are easily expressed using overt quantification over possibilia, are not expressible in quantified modal languages under the usual Kripke semantics. (E.g. ''There might have been something that actually doesn't exist''.) Several such results are proved by characterizing the set of sentences true in all models meeting such a condition and then constructing a model for that set not meeting that condition.