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Frame Based Formulas for Intermediate Logics

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Abstract

In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by Jankov-de Jongh formulas. We also show that not every intermediate logic is axiomatizable by frame based formulas.

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Correspondence to Nick Bezhanishvili.

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Bezhanishvili, N. Frame Based Formulas for Intermediate Logics. Stud Logica 90, 139–159 (2008). https://doi.org/10.1007/s11225-008-9147-0

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