User blog comment:P進大好きbot/Ordinal Notation Associated to a Proper Class of Ordinals/@comment-27513631-20180626200006/@comment-35470197-20180626214050

Since googologists usualy only accepts a computable large number defined in ZFC set theory, it is not so good to use set theory beyond ZFC set theory for the definition of an ordinal notation in order to define a computable large number.

Although there are many computable large numbers beyond ZFC such as ones using finite promise (defined in SMAH+), they are not standard here, I guess.

I note that I am working on NBG and ZFC+Inaccessible in my daily life outside googology, because I use category theory and infinity category theory. They are so good.