On Non-axiomatizability of Superintuitionistic Predicate Logics of Some Classes of Well-founded and Dually Well-founded Kripke Frames

摘要

The article presents general results on non-axiomatizability for superintuitionistic predicate logics. In particular, the logics of all well-ordered, all dually well-ordered, and all dually well-founded Kripke frames (in the semantics with nested and with constant domains) are Π_1~1-hard, and the logic of all Kripke frames of finite height is not recursively axiomatizable (although it is known to be Π_2~0-arithmetical). A result on Kripke-incompleteness is stated as well.