User blog comment:Scorcher007/S - Large Countable Ordinal Notation. Chapter I, Up to KPm./@comment-31580368-20190912145823/@comment-35470197-20190912150432

Right, you should use L. But you still have a mistake. KP set theories are not something like KP augumented by "the universe is α" or "the universe is L_α" for some ordinal α.