User blog comment:ArtismScrub/Hierarchical Cardinal Notation (HCN)/@comment-80.98.179.160-20180227124011/@comment-32783837-20180227194710

Because using collapsing ordinals goes much further.

φ(ΩΩ,0) is already the first fixed point of α ↦ φ(1,0,0,0,0,...,0,0,0,0) with α "0"s. The equivalent of that in THIS notation is Φ(𝐈𝐈,0), and this can of course go much, much, much further.