The Kuznetsov-Gerčiu and Rieger-Nishimura logics

Logic and Logical Philosophy 17 (1-2):73-110 (2008)
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We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on [9]. Furthermore, for each function f: omega -> omega, we construct an extension Lf of KG such that Lf has the fmp, but does not have the f-size model property. We also give a new simple proof of another result of Gerčiu [9] characterizing the only extension of KG that bounds the fmp for extensions of KG. We conclude the paper by proving that RN.KC = RN + (¬p vee ¬¬p) is the only pre-locally tabular extension of KG, introduce the internal depth of an extension L of RN, and show that L is locally tabular if and only if the internal depth of L is finite



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Author Profiles

Nick Bezhanishvili
University of Amsterdam
Dick De De Jongh
University of Amsterdam

References found in this work

Prefinitely axiomatizable modal and intermediate logics.Marcus Kracht - 1993 - Mathematical Logic Quarterly 39 (1):301-322.
On the Lattice Theory of Brouwerian Propositional Logic.Ladislav Rieger - 1952 - Journal of Symbolic Logic 17 (2):146-147.

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