On the  second order intuitionistic propositional logic without a universal quantifier

old_uid5612
titleOn the  second order intuitionistic propositional logic without a universal quantifier
start_date2008/11/17
schedule14h-16h
onlineno
summaryWe examine second order intuitionistic propositional logic, IPC2. Let F9 be the set of formulas with no universal quantification. We prove Glivenko’s theorem for formulas in F9 that is, for ' 2 F9, ' is a classical tautology if and only if ¬¬' is a tautology of IPC2. We show that for each sentence ' 2 F9 (without free variables), ' is a classical tautology if and only if ' is an intuitionistic tautology. As a corollary we obtain a semantic argument that the quantifier 8 is not definable in IPC2 from ?,_,^,!, 9.
responsiblesBonnay, Sandu