D. de Jongh
- Jankov's theorems for intermediate logics in the setting of universal models
- Lecture Notes in Computer Science
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
In this article we prove two well-known theorems of Jankov in a uniform frame-theoretic manner. In frame-theoretic terms, the first one states that for each finite rooted intuitionistic frame there is a formula ψ with the property that this frame can be found in any counter-model for ψ in the sense that each descriptive frame that falsifies ψ will have this frame as the p-morphic image of a generated subframe (). The second one states that KC, the logic of weak excluded middle, is the strongest logic extending intuitionistic logic IPC that proves no negation-free formulas beyond IPC (). The proofs use a simple frame-theoretic exposition of the fact discussed and proved in  that the upper part of the n-Henkin model H(n)(n) is isomorphic to the n-universal model U(n)(n) of IPC. Our methods allow us to extend the second theorem to many logics L for which L and L + KC prove the same negation-free formulas. All these results except the last one earlier occurred in a somewhat different form in .
- go to publisher's site
- Proceedings title: Logic, Language and Computation: 8th International Tbilisi Symposium on Logic, Language, and Computation,
TbiLLC 2009, Bakuriani, Georgia, September 21-25, 2009: revised selected papers
Place of publication: Heidelberg
Editors: N. Bezhanishvili, S. Loebner, K. Schwabe, L. Spada
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