X-2013-01: The Universal Model for the Negation-free Fragment of IPC

X-2013-01: Tzimoulis, Apostolos and Zhao, Zhiguang (2013) The Universal Model for the Negation-free Fragment of IPC. [Report]

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Abstract

We identify the universal n-model of the negation-free fragment of the intuitionistic propositional calculus IPC. We denote it by U*(n) and show that it is isomorphic to a generated submodel of the universal n-model of IPC, which is denoted by U(n). We show that this close resemblance makes U*(n) mirror many properties of U(n). Finally, using U*(n), we give an alternative proof of Jankov's Theorem that the intermediate logic KC, the logic of the weak excluded middle, is the greatest intermediate logic extending IPC that proves exactly the same negation-free formulas as IPC.

Item Type: Report
Report Nr: X-2013-01
Series Name: Technical Notes (X) Series
Year: 2013
Uncontrolled Keywords: universal models; fragment of intuitionistic logic; Jankov's theorem
Subjects: Logic
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/688

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