Intermediate Logics and Visser's Rules

Rosalie Iemhoff
Utrecht University
Visser's rules form a basis for the admissible rules of . Here we show that this result can be generalized to arbitrary intermediate logics: Visser's rules form a basis for the admissible rules of any intermediate logic for which they are admissible. This implies that if Visser's rules are derivable for then has no nonderivable admissible rules. We also provide a necessary and sufficient condition for the admissibility of Visser's rules. We apply these results to some specific intermediate logics and obtain that Visser's rules form a basis for the admissible rules of, for example, De Morgan logic, and that Dummett's logic and the propositional Gödel logics do not have nonderivable admissible rules
Keywords intermediate logics   intuitionistic logic   admissible rules   projective formulas
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DOI 10.1305/ndjfl/1107220674
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References found in this work BETA

Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
A Characterization of Intuitionistic Propositional Logic.Rosalie Iemhoff - 2001 - Annals of Pure and Applied Logic 113 (1-3):161-173.

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Citations of this work BETA

Consequence Relations and Admissible Rules.Rosalie Iemhoff - 2016 - Journal of Philosophical Logic 45 (3):327-348.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
Complexity of Admissible Rules.Emil Jeřábek - 2007 - Archive for Mathematical Logic 46 (2):73-92.
Independent Bases of Admissible Rules.Emil Jerábek - 2008 - Logic Journal of the IGPL 16 (3):249-267.

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