Eliya Cohen

A variable domain model theory with accessibility is developed to interpret the language of second-order propositional modal logic. It is shown that propositionally quantified modal logics S5 and weaker as characterized by the classes of such frames are recursively isomorphic to second-order logic and thus not recursively axiomatizable. The result is then extended to a related class of logics validating a higher-order comprehension principle. While the primary objective of this paper is to explore formal systems, many of the model-theoretic decisions are informed by contingentist views. Given the attention to higher-order formal arguments against contingentism, the results of this paper might be of some interest to those concerned with that debate.