Finite Axiomatizability of Transitive Logics of Finite Depth and of Finite Weak Width

Abstract

This paper presents a study of the finite axiomatizability of transitive logics of finite depth and finite weak width. We prove the finite axiomatizability of each transitive logic of finite depth and of weak width $1$ that is characterized by rooted transitive frames in which all antichains contain at most $n$ irreflexive points. As a negative result, we show that there are non-finitely-axiomatizable transitive logics of depth $n$ and of weak width $k$ for each $n\geqslant3$ and $k\geqslant2$.