Description

• Title:
  The Kuznetsov-Gerčiu and Rieger-Nishimura logics
• Creator:
  Bezhanishvili, Guram;
  Bezhanishvili, Nick;
  de Jongh, Dick
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2008.06.19
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 17 No. 1-2 (2008); 73-110;
  Logic and Logical Philosophy; Tom 17 Nr 1-2 (2008); 73-110;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2008.006/1303
• Subject:
  intermediate logics;
  Heyting algebras;
  finite model property;
  Mathematics Subject Classification;
  Primary 03B55;
  Secondary 06D20
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2008.006
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text