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

Studies in Logic, Vol. 12, No. 3 (2019): 16–31                PII: 1674-3202(2019)-03-0016-16

Yan Zhang

Abstract. This paper presents a study of 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 are characterized by rooted transitive frames in which all antichains contain at most n irreflexive points. As to negative results, we show that there are non-finitely-axiomatizble transitive logics of depth n and of weak width k for each n ⩾ 3 and k ⩾ 2.