NOTE: This is a work on hiatus, due to the discussion in the comments. I might work on it if i reconsider. NOTE: I will not respond to any comments which starts asking me pure nonsense about defining things. So don't bother.
Recently, i have been trying to find a way to determine the growth rate of KthulhuHimself's Lib(n) function. So i came up with something called Hyper-countable ordinals. Here i explain how it works and it's respective extensions.
Hyper-countable Ordinal Hierarchy