Degree of Kripke-incompleteness of Tense Logics

Author: Qian Chen
Preprint: arXiv:2507.04533.

Abstract

The degree of Kripke-incompleteness of a logic $L$ in a lattice $\mathcal{L}$ of logics is the cardinality of the logics in $\mathcal{L}$ that share the same class of Kripke frames with $L$. This preprint generalizes Blok’s dichotomy theorem from $\mathsf{NExt}(\mathsf{K})$ to lattices of tense logics, including $\mathsf{K}_t$, the lattice of all tense logics, and $\mathsf{NExt}(\mathsf{S4}_t)$. It also shows that, in these lattices, iterated splittings are exactly the strictly Kripke-complete logics.

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