Tabularity and Post-completeness in Tense Logic

Authors: Qian Chen and Minghui Ma
Published in: The Review of Symbolic Logic 17(2):475–492 (2024). DOI: https://doi.org/10.1017/S1755020322000132

Abstract

A new characterization of tabularity in tense logic is established, namely, a tense logic $L$ is tabular if and only if $\mathsf{tab}_n^T\in L$ for some $n\geq 1$. Two characterization theorems for the Post-completeness in tabular tense logics are given. Furthermore, a characterization of the Post-completeness in the lattice of all tense logics is established. Post numbers of some tense logics are shown.