User blog comment:MachineGunSuper/The Infinity Generator/@comment-32783837-20180114152424

Your ALEPHEN is called the omega fixed point.

It seems to me that an obvious continuation here would be Ԓ(1,0), so we can say that:

Ԓ(α,0) is the αth fixed point of β ↦ ℵβ.

and continue from there somehow