Abstract
There are several known Lindström-style characterization results for basic modal logic. This paper proves a generic Lindström theorem that covers any normal modal logic corresponding to a class of Kripke frames definable by a set of formulas called strict universal Horn formulas. The result is a generalization of a recent characterization of modal logic with the global modality. A negative result is also proved in an appendix showing that the result cannot be strengthened to cover every first-order elementary class of frames. This is shown by constructing an explicit counterexample.
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Enqvist, S. A General Lindström Theorem for Some Normal Modal Logics. Log. Univers. 7, 233–264 (2013). https://doi.org/10.1007/s11787-013-0078-9
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DOI: https://doi.org/10.1007/s11787-013-0078-9