User blog comment:PsiCubed2/For Newbies (and Veterans too): The Great Scale of Googology/@comment-25601061-20171219161544/@comment-30754445-20171221115456

The Other Wiki = the ordinary wikipedia.

Don't recall were I've first seen this term (apparently, given your baffled response, not here), but I've used it on wikias ever since.

At any rate, mathjax is known to randomly break and fix itself in the comments sections, For me its still broken (I still can't see you post properly) but it doesn't matter. I've got the gist of what you're saying.

I'm still confused though.

Let's say we use bigger and bigger "naive computable" extensions of  ω1CK:

ω1CK+1

ω1CKx2

ω1CK ↑ 2

ω1CK ↑ ω1CK

φ(1,ω1CK+1)

and so on.

What's the supermum of all these possible extensions? From what you're saying, I gather that this would be far far less then ω2CK. But does this ordinal have a name? Are there standard notations that deal with such ordinals?

I'm simply trying to understand the "landscape" between ω1CK and ω2CK better.

And another question: Is there an analogue to the BB function that gives us an ω2CK growth rate?