  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 $k\geqslant2$.
