PP-2010-08: Jankov's Theorems for Intermediate Logics in the Setting of Universal Models

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

[thumbnail of Full Text]
Preview
Text (Full Text)
PP-2010-08.text.pdf

Download (130kB) | Preview
[thumbnail of Abstract] Text (Abstract)
PP-2010-08.abstract.txt

Download (1kB)

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

Actions (login required)

View Item View Item