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Linear Kripke frames and Gödel logics

Published online by Cambridge University Press:  12 March 2014

Arnold Beckmann
Department of Computer Science, University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, UK. E-mail:
Norbert Preining
Dipartimento di Scienze Matematiche, Università di Siena, 53100 Siena, Italy. E-mail:


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.

Research Article
Copyright © Association for Symbolic Logic 2007

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