User blog comment:Ubersketch/A universal notation/@comment-36957202-20181225213307/@comment-35470197-20181226233734

I heard that the existence of a recursive notation/hierarchy based on ordinals, i.e. well-ordered, which goes beyond any total computable functions is an open problem in mathematics, which is believed to be false. Therefore using ordinals is not so good. Usually we need a well-founded but not well-ordered hierarchy.