User blog comment:Ubersketch/Large Cardinals vs. Non-recursive Ordinals vs. Stages/@comment-35470197-20190102084640

I note that UNOCF is not formalised even below large cardinal levels. For example, there is no formalisation applicable to any ordinals below \(\psi_0(\Omega_{\omega})\). (Only specific ordinals can be presented in the notation.)

Another problem is that few active googologists understands the difference between OCFs and associated ordinal notation systems.

> Non-recursive ordinals; This one is much newer but has a lot of support.

Well, it is false. Non-recursive ordinals simultaneously appeared with large cardinals in the study of ordinal analysis. It was traditionally used in order to reduce the argument of OCFs with with large cardinals to that in ZFC set theory.