@article{Bezhanishvili_Bezhanishvili_de Jongh_2008, title={The Kuznetsov-Gerčiu and Rieger-Nishimura logics}, volume={17}, url={https://apcz.umk.pl/LLP/article/view/LLP.2008.006}, DOI={10.12775/LLP.2008.006}, abstractNote={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.}, number={1-2}, journal={Logic and Logical Philosophy}, author={Bezhanishvili, Guram and Bezhanishvili, Nick and de Jongh, Dick}, year={2008}, month={Jun.}, pages={73–110} }