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2018 Stable Formulas in Intuitionistic Logic
Nick Bezhanishvili, Dick de Jongh
Notre Dame J. Formal Logic 59(3): 307-324 (2018). DOI: 10.1215/00294527-2017-0030

Abstract

In 1995 Visser, van Benthem, de Jongh, and Renardel de Lavalette introduced NNIL-formulas, showing that these are (up to provable equivalence) exactly the formulas preserved under taking submodels of Kripke models. In this article we show that NNIL-formulas are up to frame equivalence the formulas preserved under taking subframes of (descriptive and Kripke) frames, that NNIL-formulas are subframe formulas, and that subframe logics can be axiomatized by NNIL-formulas. We also define a new syntactic class of ONNILLI-formulas. We show that these are (up to frame equivalence) the formulas preserved in monotonic images of (descriptive and Kripke) frames and that ONNILLI-formulas are stable formulas as introduced by Bezhanishvili and Bezhanishvili in 2013. Thus, ONNILLI is a syntactically defined set of formulas axiomatizing all stable logics. This resolves a problem left open in 2013.

Citation

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Nick Bezhanishvili. Dick de Jongh. "Stable Formulas in Intuitionistic Logic." Notre Dame J. Formal Logic 59 (3) 307 - 324, 2018. https://doi.org/10.1215/00294527-2017-0030

Information

Received: 18 August 2014; Accepted: 2 December 2015; Published: 2018
First available in Project Euclid: 4 May 2018

zbMATH: 06939322
MathSciNet: MR3832083
Digital Object Identifier: 10.1215/00294527-2017-0030

Subjects:
Primary: 03B20, 03B55

Rights: Copyright © 2018 University of Notre Dame

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Vol.59 • No. 3 • 2018
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