2015•arXiv (Cornell University)Open access

On the number of variables in undecidable superintuitionistic\n propositional calculi

Grigoriy V. Bokov

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Abstract

In this paper, we construct an undecidable 3-variable superintuitionistic\npropositional calculus, i.e., a finitely axiomatizable extension of the\nintuitionistic propositional calculus with axioms containing only 3 variables.\nSince there are no 2-variable superintuitionistic propositional calculi, this\nis the minimal possible number of variables.\n

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In this paper, we construct an undecidable 3-variable superintuitionistic\npropositional calculus, i.e., a finitely axiomatizable extension of the\nintuitionistic propositional calculus with axioms containing only 3 variables.\nSince there are no 2-variable superintuitionistic propositional calculi, this\nis the minimal possible number of variables.\n

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Available abstract

In this paper, we construct an undecidable 3-variable superintuitionistic\npropositional calculus, i.e., a finitely axiomatizable extension of the\nintuitionistic propositional calculus with axioms containing only 3 variables.\nSince there are no 2-variable superintuitionistic propositional calculi, this\nis the minimal possible number of variables.\n

Key concepts: Undecidable problem, Propositional variable, Propositional formula, Propositional calculus, Mathematics, Axiom, Well-formed formula, Variable (mathematics)

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