User blog comment:TheKing44/The Grand Finale Functions/@comment-35470197-20190609062821

The original definition is not regarded as googology in first order set theory. I agree that several googologists regard it as a function in ZFC although it is not formalisable, but it is not what Rayo himself intended. (Such confusion might have occurred by the lack of the declaration of the precise axiom under which Rayo worked.)