Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A study of intermediate propositional logics on the third slice

  • 32 Accesses

  • 1 Citations


The intermediate logics have been classified into slices (cf. Hosoi [1]), but the detailed structure of slices has been studied only for the first two slices (cf. Hosoi and Ono [2]). In order to study the structure of slices, we give a method of a finer classification of slices & n (n ≥ 3). Here we treat only the third slice as an example, but the method can be extended to other slices in an obvious way. It is proved that each subslice contains continuum of logics. A characterization of logics in each subslice is given in terms of the form of models.

This is a preview of subscription content, log in to check access.


  1. [1]

    T. Hosoi,On intermediate logics I,J. Fac. Sci., Univ. Tokyo 14 (1967), pp. 293–312.

  2. [2]

    T. Hosoi andH. Ono,The intermediate logics on the second slice,J. Fac. Sci. 17 (1970), pp. 457–461.

  3. [3]

    V. A. Jankov,Constructing a sequence of strongly independent superintuitionistic propositional calculi,Soviet Math. Dokl. 9 (1968), pp. 806–807.

  4. [4]

    Y. Komori,The finite model property of the intermediate propositional logics on finite slices,J. Fac. Sci., Univ. Tokyo 45 (1975), pp. 117–120.

  5. [5]

    C. G. McKay,On finite logics,Indagationes mathematicae 29 (1967), pp. 363–365.

  6. [6]

    H. Ono,Kripke models and intermediate logics,Publ. RIMS, Kyoto Univ. 6 (1970/71), pp. 461–476.

  7. [7]

    H. Ono,Some results on the intermediate logics,Publ. RIMS, Kyoto Univ. 8 (1972), pp. 117–130.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hosoi, T., Masuda, I. A study of intermediate propositional logics on the third slice. Stud Logica 52, 15–21 (1993). https://doi.org/10.1007/BF01053061

Download citation


  • Mathematical Logic
  • Detailed Structure
  • Computational Linguistic
  • Propositional Logic
  • Fine Classification