User blog comment:P進大好きbot/ZFC-variant of Rayo's number/@comment-36957202-20190517203742/@comment-35470197-20190517221247

Thanks. The reason why I used \(n \uparrow^{n} n\) is because \(\textrm{CoRayo}\) grows very slowly when \(n\) is very small. If you replace \(n \uparrow^{n} n\) by \(n\), it will not essentially change the growth rate.

The cumulative hierarchy is the hierarchy of von Neuman universe. For example, you can see the definition here.