On non-axiomatizability of superintuitionistic predicate logics of some classes of well-founded and dually well-founded kripke frames
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 [see text for formula]-hard, and the logic of all Kripke frames of finite height is not recursively axiomatizable (although it is known to be [see text for formula]-arithmetical). A result on Kripke-incompleteness is stated as well.
superintuitionistic predicate logics recursive axiomatizability pi(1)(1) -hardness kripke semantics