Second order propositional operators over cantor space

Abstract

We consider propositional operators defined by propositional quantification in intuitionistic logic. More specifically, we investigate the propositional operators of the formA* :p ↦ ∃q(p ≡A(q)) whereA(q) is one of the following formulae: (¬¬q →q) V ¬¬q, (¬¬q →q) → (¬¬q V ¬q), ((¬¬q →q) → (¬¬q V ¬q)) → ((¬¬q →q) V ¬¬q). The equivalence ofA*(p) to ¬¬p is proved over the standard topological interpretation of intuitionistic second order propositional logic over Cantor space.