Help Me Understand Ordinals Beyond the BHO

I would really like to learn how the ordinals go beyond the BHO and especially, beyond ψ(Ω_ω).

I've read Deedlit's six-part guide, but after much effort, I still don't really "get" how it works.

Any help will be appreciated, and my own efforts - as I learn - will be posted here.

Thanks

Psi