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    Braüner, Torben and Ghilardi, Silvio 2007. Handbook of Modal Logic.


The superintuitionistic predicate logic of finite Kripke frames is not recursively axiomatizable

  • Dmitrij Skvortsov (a1)
  • DOI:
  • Published online: 01 March 2014

We prove that an intermediate predicate logic characterized by a class of finite partially ordered sets is recursively axiomatizable iff it is “finite”, i.e., iff it is characterized by a single finite partially ordered set. Therefore, the predicate logic LFin of the class of all predicate Kripke frames with finitely many possible worlds is not recursively axiomatizable.

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[3]T. Shimura , Kripke completeness of some intermediate predicate logics with the axiom of constant domain and a variant of canonical formulas, Studia Logica, vol. 52 (1993), no. 1, pp. 2340.

[5]D. Skvortsov , On the predicate logic of finite Kripke frames, Studia Logica, vol. 54 (1995), pp. 7988.

[6]D. Skvortsov , Not every “tabular” predicate logic is finitely axiomatizable, Studia Logica, vol. 59 (1997), pp. 387396.

[8]C. A. Smoryński , Applications of Kripke models, Metamathematical investigations of intuitionistic arithmetic and analysis (A. S. Troelstra , editor). Lecture Notes in Mathematics, vol. 344, Springer-Verlag, Berlin, Heidelberg, New York, 1973, pp. 324391.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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