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Linear Kripke frames and Gödel logics

Published online by Cambridge University Press:  12 March 2014

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

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 26 - 44
Copyright
Copyright © Association for Symbolic Logic 2007

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