Uncountably many maximally consistent neighborhood complete congruential modal logics

Abstract

We solve an open problem posed by Peter Fritz in \cite{Fritz} by proving that there are uncountably many C-Post complete congruential modal logics which are neighborhood complete. The method is algebraic: we construct an uncountable sequence of varieties of modal algebras which are minimal in the lattice of all subvarieties of modal algebras and are generated by a single complete and atomic modal algebra.