Abstract
An example of finite tree Mo is presented such that its predicate logic (i.e. the intermediate predicate logic characterized by the class of all predicate Kripke frames based on Mo) is not finitely axiomatizable. Hence it is shown that the predicate analogue of de Jongh - McKay - Hosoi's theorem on the finite axiomatizability of every finite intermediate propositional logic is not true.
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Skvortsov, D. Not Every "Tabular" Predicate Logic is Finitely Axiomatizable. Studia Logica 59, 387–396 (1997). https://doi.org/10.1023/A:1005088429206
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DOI: https://doi.org/10.1023/A:1005088429206