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Studia Logica

, Volume 40, Issue 2, pp 89–98 | Cite as

Model theory for tense logic: Saturated and special models with applications to the tense hierarchy

  • Hirokazu Nishimura
Article

Abstract

The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.

In this paper we are concerned exclusively with quantifiedK1 (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].

Keywords

Mathematical Logic Special Model Model Theory Linear Time Existence Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    J. L. Bell andA. B. Slomson,Models and Ultraproducts, North Holland, 1969.Google Scholar
  2. [2]
    K. A. Bowen,Normal modal model theory,Journal of Philosophical Logic 4 (1975), pp. 97–131.Google Scholar
  3. [3]
    R. A. Bull,Algebraic study of tense logics with linear time,Journal of Symbolic Logic 33 (1968), pp. 27–38.Google Scholar
  4. [4]
    C. C. Chang andG. Keisler,Model Theory, North-Holland, 1973.Google Scholar
  5. [5]
    K. Fine,Model theory for modal logic — Part 1,Journal of Philosophical Logic 7 (1978), pp. 125–156.Google Scholar
  6. [6]
    D. M. Gabbay,Model theory for tense logics,Annals of Mathematical Logic 8 (1975), pp. 185–236.Google Scholar
  7. [7]
    D. M. Gabbay,Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics, D. Reidel, 1976.Google Scholar
  8. [8]
    A. N. Prior,Past, Present and Future, Clarendon, Oxford, 1967.Google Scholar
  9. [9]
    N. Rescher andA. Urquhart,Temporal Logic, Springer-Verlag, 1971.Google Scholar

Copyright information

© Polish Academy of Sciences 1981

Authors and Affiliations

  • Hirokazu Nishimura
    • 1
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan

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