深度和弱宽度有穷的传递逻辑的有穷可公理化（英文）

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

这篇文章研究深度和弱宽度都有穷的传递逻辑类的可有穷公理化问题,并给出了正反两方面的结论。在正面方面,本文证明了对每个深度有穷且弱宽度为1的传递逻辑L,如果L 的框架中反链的禁自返点基数都不大于某个自然数n,那么L 是有穷可公理化的。对于反面结论,本文证明了对任意n≥ 3 和k ≥ 2,存在深度为n 且弱宽度为k 的传递逻辑是不可有穷公理化的。

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.