Duality between modal algebras and neighbourhood frames (Q1825863)

This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras, i.e. Boolean algebras with an additional unary operation. These results extend results of \textit{R. I. Goldblatt} [Rep. Math. Logic 6, 41-77 (1976; Zbl 0356.02016); ibid. 7, 21-52 (1976; Zbl 0356.02017)] and \textit{S. K. Thomason} [J. Symb. Logic 40, 439-442 (1975; Zbl 0317.02012)] about categories of relational frames for modal logic. The exact connexion between general relational frames and general neighbourhood frames is investigated, and morphisms appropriate to the latter, which generalize p-morphisms, are defined.