Linear Kripke Frames and Gödel Logics

Journal of Symbolic Logic 72 (1):26 - 44 (2007)
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Abstract

We investigate the relation between intermediate predicate logics based on countable linear Kripke frames with constant domains and Gödel logics. We show that for any such Kripke frame there is a Gödel logic which coincides with the logic defined by this Kripke frame on constant domains and vice versa. This allows us to transfer several recent results on Gödel logics to logics based on countable linear Kripke frames with constant domains: We obtain a complete characterisation of axiomatisability of logics based on countable linear Kripke frames with constant domains. Furthermore, we obtain that the total number of logics defined by countable linear Kripke frames on constant domains is countable

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Citations of this work

First-order Gödel logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
ŁΠ logic with fixed points.Luca Spada - 2008 - Archive for Mathematical Logic 47 (7-8):741-763.
Note on witnessed Gödel logics with Delta.Matthias Baaz & Oliver Fasching - 2010 - Annals of Pure and Applied Logic 161 (2):121-127.

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