User blog comment:P進大好きbot/Full References of Arguments on Ordinal Notations with Large Cardinals/@comment-25601061-20180729214112

I don't use any specific choice of axioms when analyzing and I haven't ever used any. I have tried to do ordinal analysis of Z2 though (although I didn't make much progress and eventually gave up on it), and I might try doing an analysis using ZFC in the future.