Infinitary combinatorics and modal logic

Journal of Symbolic Logic 55 (2):761-778 (1990)
We show that the modal propositional logic G, originally introduced to describe the modality "it is provable that", is also sound for various interpretations using filters on ordinal numbers, for example the end-segment filters, the club filters, or the ineffable filters. We also prove that G is complete for the interpretation using end-segment filters. In the case of club filters, we show that G is complete if Jensen's principle □ κ holds for all $\kappa ; on the other hand, it is consistent relative to a Mahlo cardinal that G be incomplete for the club filter interpretation
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DOI 10.2307/2274663
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Leo Esakia (2004). Intuitionistic Logic and Modality Via Topology. Annals of Pure and Applied Logic 127 (1-3):155-170.
Daniele Mundici (1998). Foreword. Studia Logica 61 (1):1-1.

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