2016•Logic Journal of IGPLRequires access

On the number of variables in undecidable superintuitionistic propositional calculi

Grigoriy V. Bokov

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Abstract

In this article, we construct an undecidable superintuitionistic propositional calculus using 3-variable axioms, i.e. an undecidable finitely axiomatizable extension of the intuitionistic propositional calculus with axioms containing only 3 variables. Since superintuitionistic propositional calculi cannot be axiomatized using less than 3 variables, this is the minimal possible number of variables.

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What this paper is about

In this article, we construct an undecidable superintuitionistic propositional calculus using 3-variable axioms, i.e. an undecidable finitely axiomatizable extension of the intuitionistic propositional calculus with axioms containing only 3 variables. Since superintuitionistic propositional calculi cannot be axiomatized using less than 3 variables, this is the minimal possible number of variables.

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Available abstract

In this article, we construct an undecidable superintuitionistic propositional calculus using 3-variable axioms, i.e. an undecidable finitely axiomatizable extension of the intuitionistic propositional calculus with axioms containing only 3 variables. Since superintuitionistic propositional calculi cannot be axiomatized using less than 3 variables, this is the minimal possible number of variables.

Key concepts: Undecidable problem, Propositional variable, Propositional formula, Axiom, Propositional calculus, Mathematics, Extension (predicate logic), Calculus (dental)

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