An extension of Jónsson‐Tarski representation and model existence in predicate non‐normal modal logics

In this paper, we give an extension of the J\'{o}nsson-Tarski representation theorem for both normal and non-normal modal algebras so that it preserves countably many infinitary meets joins. To extend to consider neighborhood frames instead Kripke just as Do\v{s}en's duality algebras, deal with infinite joins, make use Q-filters prime filters. Then, show every predicate logic, whether is or non-normal, has a model defined on frame constant domains, completeness some logics. We also same results