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