PP-2010-08:
de Jongh, Dick and Yang, Fan
(2010)
*Jankov's Theorems for Intermediate Logics in the Setting of Universal Models.*
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## Abstract

In this article we prove the Jankov Theorem for extensions of IPC

([6]) and the Jankov Theorem for KC ([7]) in a uniform frame-theoretic

way in the setting of n-universal models for IPC. In frame-theoretic

terms, the first Jankov Theorem states that for each finite rooted

frame there is a formula \psi with the property that any counter-model

for \psi needs this frame in the sense that each descriptive frame

that falsifies \psi will have this frame as the p-morphic image of a

generated subframe. The second one states that KC is the strongest

logic that proves no negationless formulas beyond IPC. On the way we

give a simple proof of the fact discussed and proved in [1] that the

upper part of the n-Henkin model H(n) is isomorphic to the n-universal

model U(n) of IPC. All these results earlier occurred in a somewhat

different form in [8].

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

Report Nr: | PP-2010-08 |

Series Name: | Prepublication (PP) Series |

Year: | 2010 |

Uncontrolled Keywords: | Intermediate Logic; Jankov's theorem; Universal Models |

Depositing User: | Prof. Dick de Jongh |

Date Deposited: | 12 Oct 2016 14:37 |

Last Modified: | 12 Oct 2016 14:37 |

URI: | https://eprints.illc.uva.nl/id/eprint/387 |

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