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On some ascending chains of brouwerian modal logics

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Abstract

This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT +2 and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of “generalized” Segerberg logics can be constructed from eachT +n logic (n ⩾ 2). The set containing allT +n and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered setΓ isω *(ω + 1). Throughout the paper my approach is fundamentally semantical.

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References

  1. K. Fine, An ascending chain ofS4 logics,Theoria 40 (1974), pp. 110–16.

    Google Scholar 

  2. G. E. Hughes, B(S4, 3, S4) unveiledTheoria, 41 (1975), pp. 11–34.

    Google Scholar 

  3. —,Omnitemporal logic and modal time,Reports on Mathematical Logic 8 (1977), pp. 41–61.

    Google Scholar 

  4. G. E. Hughes andM. J. Cresswell,An Introduction to Modal Logic. London: Methuen and Co., Ltd., 1968.

    Google Scholar 

  5. —,Omnitemporal logic and converging time,Theoria, 41 (1975), pp. 11–34.

    Google Scholar 

  6. N. Rescher, andA. Urquahart,Temporal Logic. Vienna and New York: Springer-Verlag, 1971.

    Google Scholar 

  7. K. Segerberg,An Essay in Classical Modal Logic. 3 volumes. Filosofika Studier, Nr 13. Uppsala: Philosophical Society and Department of Philosophy, University of Uppsala, Sweden, 1971.

    Google Scholar 

  8. -Disproof of a conjecture of Rescher and Urquhart, inP and Q: Mini-essays in Honor of Risto Hilpinen, Åbo Publication of the Group in Logic and Methodology of Real Finland, 1973.

  9. W. Sierpiński,Cardinal and Ordinal Numbers, 2nd ed., rev. Warsaw and New York: Państwowe Wydawnictwo Naukowe, 1965.

    Google Scholar 

  10. I. Thomas,Modal systems in the neighborhood of T,Notre Dame Journal of Formal Logic 5 (1964), pp. 59–61.

    Google Scholar 

  11. B. C. van Fraassen,Formal Semantics and Logic, New York and London: The Macmillan Company, 1971.

    Google Scholar 

  12. M. M. Zuckerman,Sets and Transfinite Numbers, New York and London: Macmillan Publishing Co., Inc. and Collier Macmillan Publishers. 1974.

    Google Scholar 

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I should like to thank Professor G. E. Hughes for helpful comments on an earlier draft of this paper.

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White, M.J. On some ascending chains of brouwerian modal logics. Stud Logica 40, 75–87 (1981). https://doi.org/10.1007/BF01837557

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