Linear Kripke frames and Gödel logics

Arnold Beckmann, Norbert Preining
2007 Journal of Symbolic Logic (JSL)  
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
more » ... 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.
doi:10.2178/jsl/1174668382 fatcat:solhhpxg6zf6nj6yndfuquv23a