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Reports on Mathematical Logic

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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.

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