Abstract
We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing the McKinsey-Tarski theorem. As a consequence, we obtain that each intermediate logic with the finite model property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.
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Dedicated to Leo Esakia on his 75th birthday. David Gabelaia’s research was supported by the Georgian National Science Foundation Grant for Young Researchers # 148.
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Bezhanishvili, G., Gabelaia, D. Connected modal logics. Arch. Math. Logic 50, 287–317 (2011). https://doi.org/10.1007/s00153-010-0214-7
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DOI: https://doi.org/10.1007/s00153-010-0214-7