Second order propositional operators over Cantor space

Studia Logica 53 (1):93 - 105 (1994)
Abstract
We consider propositional operators defined by propositional quantification in intuitionistic logic. More specifically, we investigate the propositional operators of the form $A^{\ast}\colon p\mapsto \exists q)$ where A is one of the following formulae: $\vee \neg \neg q,\rightarrow ,\rightarrow )\rightarrow \vee \neg \neg q)$ . The equivalence of $A^{\ast}$ to $\neg \neg p$ is proved over the standard topological interpretation of intuitionistic second order propositional logic over Cantor space. We relate topological interpretations of second order intuitionistic propositional logic over Cantor space with the interpretation of propositional quantifiers suggested by A. Pitts. One of the merits of Pitts' interpretation is shown to be valid for the interpretation over Cantor space
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