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Modal logics with no minimal proper extensions

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Abstract

We show that neither the descending chain property nor the finite model property is a necessary condition for a model logic having no minimal proper extension. This answers in the negative two questions raised by G. E. Hughes.

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References

  1. G. E. Hughes, Modal systems with no minimal proper extensions, Reports on Mathematical Logic 6 (1976), pp. 93–98.

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  2. E. J. Lemmon and D. Scott, Intensional Logic. Preliminary draft of initial chapters by E. J. Lemmon, mimeographed, July 1966.

  3. D. Makinson, A normal modal calculus between T and S4 without the finite model property, Journal of Symbolic Logic 34 (1969), pp. 35–38.

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Authors and Affiliations

  1. Ohio State University, Columbus, USA

    George F. Schumm

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  1. George F. Schumm
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Schumm, G.F. Modal logics with no minimal proper extensions. Stud Logica 38, 233–235 (1979). https://doi.org/10.1007/BF00405381

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  • DOI: https://doi.org/10.1007/BF00405381

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