Abstract

In this paper second order intuitionistic propositional logic and its interpretation over Cantor space are considered. We focus on the propositional operators of the form $A^{*}=\exists q )$ where $A$ is a monadic propositional formula in the standard language $\{\neg, \vee, \wedge, \rightarrow \}$. It is shown that, over Cantor space, all operators $A^{*}$ are equivalent to appropriate formulae in $\{\neg, \vee, \wedge, \rightarrow \}$ with the only variable $p$. The coincidence, while restricting to the operators $A^{*}$, of topological interpretation over Cantor space and Pitts' interpretation of propositional quantifiers is obtained as a corollary.