A Remark on Superintuitionistic Predicate Logics of Kripke Frames with Constant and with Nested Domains

The superintuitionistic predicate logics (without or with equality) of all predicate Kripke frames with nested domains over a fixed poset W (a set of possible worlds) are embeddable in the logic (without equality) of all Kripke frames with constant domains over W. Therefore, Takano's result [13] on finite axiomatizability of the logic of Kripke frames with constant domains over the set of real numbers implies the recursive axiomatizability of the corresponding logics with nested domains. Other consequences are mentioned as well.