User blog comment:ArtismScrub/Hierarchical Cardinal Notation (HCN)/@comment-2001:56A:71A8:5F00:F08D:F231:25D0:7461-20180228031656

Φ(1,0) = α -> Φ(0,α) = α -> Ωα = ψI(0)

Φ(1,1) = ψI(1)

Φ(1,w) = ψI(w)

...

Φ(2,0) = α -> Φ(1,α) = α -> ψI(α) = I

Φ(2,1) = I2

Φ(3,0) = α -> Iα = II I... = ψI(1,0)(0) (I'm not sure of the comparisons past here)

Φ(4,0) = I(1,0)

Φ(5,0) = ψI(2,0)(0)

Φ(6,0) = I(2,0)