PP-2008-11:
Bezhanishvili, Guram and Bezhanishvili, Nick and de Jongh, Dick
(2008)
*The Kuznetsov-Gerciu and Rieger-Nishimura Logics: The Boundaries of the Finite Model Property.*
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## Abstract

We give a systematic method of constructing extensions of the

Kuznetsov- Gerciu 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 Gerciu's result 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 [Gerciu]. 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 Gerciu 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 v ¬¬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.

Item Type: | Report |
---|---|

Report Nr: | PP-2008-11 |

Series Name: | Prepublication (PP) Series |

Year: | 2008 |

Uncontrolled Keywords: | superintuitionistic logic, finite model property, descriptive frames |

Subjects: | Logic |

Depositing User: | Prof. Dick de Jongh |

Date Deposited: | 12 Oct 2016 14:36 |

Last Modified: | 12 Oct 2016 14:36 |

URI: | https://eprints.illc.uva.nl/id/eprint/285 |

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