Hereditary Structural Completeness over K4: Rybakov’s Theorem Revisited
James Carr

Abstract:
A deductive system is said to be structurally complete if its admissible rules are derivable, and moreover is hereditarily structurally complete if all its finitary extensions are structurally complete. Citkin (1997) established a characterisation of hereditarily structurally complete intermediate logics and Rybakov (1995) gave a characterisation for transitive modal logics. Both their proofs are difficult in their own way, however recently Bezhanishvili and Moraschini (2019) gave a self-contained proof of Citkin’s result based on Esakia duality. The aim of this project is to do the same for Rybakov’s result using a duality for modal algebras. In doing so we will identify and correct for an error in Rybakov’s characterisation.