User:Vel!/pu/BAN extension?

Here is a sketch for a possible extension to BAN, and if it was defined it might reach up to ψ(ψI(0)).

Hyper-nested hierarchical hyper-nested array notation (AKA beyond nested arrays VI)
So the limit of BAN in the end is ψ(ΩΩ). The / separator has level Ω, so if you include hyperseparators on the top level in subscript, you can get uncountable ordinals in the subscript of Ω and get to ψ(ΩΩ 2 ). Then you can top that off, and so on.