PP-2016-20: Universal models for the positive fragment of intuitionistic logic

PP-2016-20: Bezhanishvili, Nick and de Jongh, Dick and Tzimoulis, Apostolos and Zhao, Zhiguang (2016) Universal models for the positive fragment of intuitionistic logic. [Report]

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Abstract

We study the n-universal model of the positive 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 n-universal model of IPC, which is denoted by U(n). We show that this close resemblance makes U*(n) mirror many properties of U(n). Using U*(n), we give an alternative proof of Jankov's theorem stating 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: PP-2016-20
Series Name: Prepublication (PP) Series
Year: 2016
Uncontrolled Keywords: Intuitionistic logic, fragments, universal models, p-morphisms
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/556

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