Journal of Symbolic Logic

Linear Kripke frames and Gödel logics

Arnold Beckmann and Norbert Preining

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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.

Article information

Source
J. Symbolic Logic, Volume 72, Issue 1 (2007), 26-44.

Dates
First available in Project Euclid: 23 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1174668382

Digital Object Identifier
doi:10.2178/jsl/1174668382

Mathematical Reviews number (MathSciNet)
MR2298469

Zentralblatt MATH identifier
1118.03016

Citation

Beckmann, Arnold; Preining, Norbert. Linear Kripke frames and Gödel logics. J. Symbolic Logic 72 (2007), no. 1, 26--44. doi:10.2178/jsl/1174668382. https://projecteuclid.org/euclid.jsl/1174668382


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