Studia Logica

, Volume 104, Issue 6, pp 1191–1204 | Cite as

Finite Frames Fail: How Infinity Works Its Way into the Semantics of Admissibility

Open Access
Article

Abstract

Many intermediate logics, even extremely well-behaved ones such as IPC, lack the finite model property for admissible rules. We give conditions under which this failure holds. We show that frames which validate all admissible rules necessarily satisfy a certain closure condition, and we prove that this condition, in the finite case, ensures that the frame is of width 2. Finally, we indicate how this result is related to some classical results on finite, free Heyting algebras.

Keywords

Intermediate logics Admissible rules Finite model property Projective Heyting algebras 

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Utrecht UniversityUtrechtThe Netherlands

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