User blog comment:Rgetar/Designation for the next element of a class above an ordinal and some rules for booster-base/@comment-35470197-20200219005322

I guess that it is a designation for a function rather than a class, because C(・) is an enumeration function. Therefore C(・)↰ α is the least ordinal greater than α and belongs to the image of C(・).

Then I do not understand the meaning of "Let Ωx = Ω• ↰ α = [c]α". Is Ω_x regarded as a function on α, while the symbol looks like a function on x?

By the way, I recommend to distinguish two distinct functions; the enumeration of weakly inaccessibles and the enumeration of weakyly inaccessibles and their limits, because there are so many googologists who are not understanding the difference.