Finite approximability as a sufficient condition for solvability in accordance with permissibility for transitive modal and super-intuitionistic logic

This paper contains a proof of solvability for permissible rules to develop any transitive modal logic possessing the property of finite approximability. Applying the Godel-McKinsey-Tarski transition we can, with due permissibility, attain solvability for any finite approximated super-intuitionistic logic.