A strong completeness theorem in intuitionistic quantified modal logic

Based on the intuitionistic first order predicate calculus H given by Thomason with the modal machinery of MIPC put forward by Prior this paper obtains the intuitionistic quantified modal logic system MIPC*, gives it a semantic interpretation and proves its strong (thus also weak) completeness theorem and soundness theorem with respect to that semantic. Since Zorn lemma plays a decisive role in our discussion, methodologically, it was even farther from the intuitionistic point of view than Thomason's result.