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

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