## Notre Dame Journal of Formal Logic

### Metalogic of Intuitionistic Propositional Calculus

Alex Citkin

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 29 September 2010

http://projecteuclid.org/euclid.ndjfl/1285765801

Digital Object Identifier
doi:10.1215/00294527-2010-031

Mathematical Reviews number (MathSciNet)
MR2741839

Zentralblatt MATH identifier
05822359

#### Citation

Citkin, Alex. Metalogic of Intuitionistic Propositional Calculus. Notre Dame J. Formal Logic 51 (2010), no. 4, 485--502. doi:10.1215/00294527-2010-031. http://projecteuclid.org/euclid.ndjfl/1285765801.

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