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

Journal of Symbolic Logic

Volumn 70, Issue 2, 2005, Pages 451-459

  Skvortsov, Dmitrij ^a  

^a All Russian Institute for Scientific and Technical Information   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 20444438416     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2178/jsl/1120224722     Document Type: Article

References (10)

1. D. M. GABBAY, Decidability of some intuitionistic predicate theories, this JOURNAL, vol. 30 (1972), pp. 579-587.
2. H. ONO. Some problems in intermediate predicate logics, Reports on Mathematical Logic, vol. 21 (1987), pp. 55-67.
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. 23-40.
4. D. SKVORTSOV, On axiomatizability of some intermediate predicate logics (summary), Reports on Mathematical Logic, vol. 22 (1988), pp. 115-116.
5. _, On the predicate logic of finite Kripke frames, Studia Logica, vol. 54 (1995), pp. 79-88.
6. _, Not every "tabular" predicate logic is finitely axiomatizable, Studio Logica, vol. 59 (1997), pp. 387-396.
7. _, On non-axiomatizability of some intermediate predicate logics, in preparation.
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. 324-391.
9. B. A. TRACHTENBROT, Impossibility of an algorithm for the decision problem infinite classes, Doklady Akademii Nauk SSSR, vol. 70 (1950), no. 4, pp. 569-572, in Russian;
10. English translation: American Mathematical Society Translations, Series 2, vol. 23 (1963), pp. 1-5.