Degree of Kripke-incompleteness of Tense Logics

2025/07/06 by Chen, Qian
#03B44 #03B45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2507.04533

Abstract

The degree of Kripke-incompleteness of a logic L in some lattice L of logics is the cardinality of logics in L which share the same class of Kripke-frames with L. A celebrated result on Kripke-incompleteness is Blok's dichotomy theorem for the degree of Kripke-incompleteness in NExt(K): every modal logic L\inNExt(K) is of the degree of Kripke-incompleteness 1 or 2^ℵ₀. In this work, we show that the dichotomy theorem for NExt(K) can be generalized to the lattices \K, \LT and \NExt(\ST) of tense logics. We also prove that in \K, \LT and \NExt(\ST), iterated splittings are exactly the strictly Kripke-complete logics.

Citations

• Degrees of the finite model property: the antidichotomy theorem

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