The Finite Model Property of Some Non-normal Modal Logics with the Transitivity Axiom

In 1997 Timothy J. Surendonk proved via algebraic semantics that all modal logics without iterative axioms are canonical and so strongly complete. In this paper, we continue the work done by Surendonk in this field. We use neighborhood semantics to show that some iterative logics (with the axiom $\mathrm{\square }p\to \mathrm{\square }\mathrm{\square }p$) are also strongly complete and have the finite model property.