On some ascending chains of brouwerian modal logics

Studia Logica 40 (1):75-87 (1981)
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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 set is *( + 1). Throughout the paper my approach is fundamentally semantical.

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10.1007/bf01837557

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References found in this work

An introduction to modal logic.G. E. Hughes - 1968 - London,: Methuen. Edited by M. J. Cresswell.
An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Temporal logic.Nicholas Rescher - 1971 - New York,: Springer Verlag. Edited by Alasdair Urquhart.
An incomplete logic containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.
An ascending chain of S4 logics.Kit Fine - 1974 - Theoria 40 (2):110-116.

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