Remarks on Stable Formulas in Intuitionistic Logic

Majid Alizadeh, Ali Bibak

DOI: http://dx.doi.org/10.12775/LLP.2018.017

Abstract


ONNILLI-formulas were introduced in [2] and were shown to be the set of formulas that are preserved under monotonic images of descriptive or Kripke frames. As a result, ONNILLI is a syntactically defined set of formulas that axiomatize all stable logics. In this paper, among other things, by proving the uniform interpolation property for ONNILLI we show that ONNILLI is exactly the set of formulas that are preserved in monotonic bijections of descriptive or (finite) Kripke models. This resolves an open problem in [2].


Keywords


intuitionistic logic; intermediate logic; subframe logics; monotonic maps; stable logics; uniform interpolation property

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References


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