## Reports on Mathematical Logic

### No. 27 (1993)

Tomasz POLACIK

OPERATORS DEFINED BY PROPOSITIONAL QUANTIFICATION AND THEIR INTERPRETATION OVER CANTOR SPACE

A b s t r a c t. 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 $A^{*}(p)=\exists q (p\equiv A(q))$ where $A(q)$ is a monadic propositional formula in the standard language $\{\neg , \vee , \wedge , \rightarrow \}$. It is shown that, over Cantor space, all operators $A^{*}(p)$ 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 (as interpolants) is obtained as a corollary.