### Metalogic of Intuitionistic Propositional Calculus

Alex Citkin
Source: Notre Dame J. Formal Logic Volume 51, Number 4 (2010), 485-502.

#### Abstract

With each superintuitionistic propositional logic L with a disjunction property we associate a set of modal logics the assertoric fragment of which is L. Each formula of these modal logics is interdeducible with a formula representing a set of rules admissible in L. The smallest of these logics contains only formulas representing derivable in L rules while the greatest one contains formulas corresponding to all admissible in L rules. The algebraic semantic for these logics is described.

First Page:
Primary Subjects: 03B55, 03F45
Secondary Subjects: 06D20
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1285765801
Digital Object Identifier: doi:10.1215/00294527-2010-031
Zentralblatt MATH identifier: 05822359
Mathematical Reviews number (MathSciNet): MR2741839

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