On Some Syntactic Properties of the Modalized Heyting Calculus

Alexei Muravitsky

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arXiv · 1612.05273

On Some Syntactic Properties of the Modalized Heyting Calculus

Alexei Muravitsky

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Abstract

We show that the modalized Heyting calculus~\cite{esa06} admits a normal axiomatization. Then we prove that in this calculus the inference rule $\square\alpha/\alpha$ is admissible (Proposition 5.6), but the rule $\square\alpha\rightarrow\alpha/\alpha$ is not (Proposition 6.1). Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.

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Alexei Muravitsky. 2016-12-15. On Some Syntactic Properties of the Modalized Heyting Calculus. https://arxiv.org/abs/1612.05273

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