Completeness of intermediate logics with doubly negated axioms

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Mathematical Logic Quarterly 60 (1-2):6-11 (2014)
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Abstract

Let denote a first‐order logic in a language that contains infinitely many constant symbols and also containing intuitionistic logic. By, we mean the associated logic axiomatized by the double negation of the universal closure of the axioms of plus. We shall show that if is strongly complete for a class of Kripke models, then is strongly complete for the class of Kripke models that are ultimately in.

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10.1002/malq.201200083

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A logic stronger than intuitionism.Sabine Görnemann - 1971 - Journal of Symbolic Logic 36 (2):249-261.
Applications of trees to intermediate logics.Dov M. Gabbay - 1972 - Journal of Symbolic Logic 37 (1):135-138.
Directed frames.Giovanna Corsi & Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (1):53-67.

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