Most properties including Kripke completeness, finite model property, and decidability are undecidable for transitive tense logics in NExt(K4t).
Chagrov (1990): Undecidable Properties of Extensions of a Provability Logic
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Most Properties are Undecidable for Transitive Tense Logics
Most properties including Kripke completeness, finite model property, and decidability are undecidable for transitive tense logics in NExt(K4t).