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

  • Dmitrij Skvortsov (a1)

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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