User blog comment:P進大好きbot/What is the greatest ordinal notation now?/@comment-1605058-20180623095923/@comment-35470197-20180623105736

Thank you very much for the detailed explanation!

Could I ask another question? There are several definitions of the proof-theoretic ordinal, so what does the definition of the proof theoretic ordinal mean in the context of googology? For example, I heard that the definition using the provability of the consistency includes a certain problem compared with the definition using the provability of the well-foundedness. (I asked several googologists who use PTOs, but they said that they do not know the definition. So I would like to know how googologists deal with PTOs...)