Uniform arithmetical completeness of modal provability logics

  • S. N. Artemov
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Literature cited

  1. 1.
    K. Gödel, “Eine Interpretation des intuitionistische Aussagenkalkuls,” Ergebnisse Math. Colloq.,4, 39–40 (1933).Google Scholar
  2. 2.
    R. M. Solovay, “Provability interpretations of modal logic,” Israel J. Math.,25, 287–304 (1976).Google Scholar
  3. 3.
    S. N. Artemov, “On modal logics which axiomatize provability,” Izv. Akad. Nauk SSSR, Ser. Mat.,49, No. 6, 1123–1154 (1985).Google Scholar
  4. 4.
    C. Smoryński, Self-Reference and Modal Logic, Springer, New York (1985).Google Scholar
  5. 5.
    F. Montagna, “On the diagonalizable algebra of Peano arithmetic,” Boll. Un. Mat. Ital. B,5, No. 16, 795–812 (1979).Google Scholar
  6. 6.
    S. N. Artemov, “Extensions of arithmetics and connected with them modal theories,” in: 6th International Congress of Logic, Methodology and Philosophy of Science. Abstracts. Secs. 1–4, Hannover (1979), pp. 15–19.Google Scholar
  7. 7.
    S. N. Artemov, “Arithmetically complete modal theories,” Semiotika Inf.,14, 115–133, VINITI, Moscow (1980).Google Scholar
  8. 8.
    A. Visser, “Aspects of diagonalization and provability,” Doctoral Thesis, Utrecht (1981).Google Scholar
  9. 9.
    G. Boolos, “Extremely undecidable sentences,” J. Symb. Logic,47, 191–196 (1982).Google Scholar
  10. 10.
    S. N. Artemov, “On uniform arithmetical completeness of provability logics,” in: 19th All-Union Algebraic Conference. L'vov. Abstracts of Lectures [in Russian], Vol. 1, L'vov (1987), p. 13.Google Scholar
  11. 11.
    A. Visser, “The provability logics ...,” J. Philos. Logic,13, 97–113 (1984).Google Scholar
  12. 12.
    G. K. Dzhaparidze, “Modal-logical means of investigating provability,” Dissertation, Candidate Philos. Sciences, Tbilisi (1986).Google Scholar
  13. 13.
    S. N. Artemov, “Superintuitionistic logics having a provability interpretation,” Dokl. Akad. Nauk SSSR,291, No. 6, 1289–1291 (1986).Google Scholar
  14. 14.
    L. D. Beklemishev, “On the classification of provability logics,” Izv. Akad. Nauk SSSR, Ser. Mat.,53, No. 5, 915–943 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • S. N. Artemov
    • 1
  1. 1.Steklov Mathematical InstituteAcademy of Sciences of the USSRUSSR

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