User blog comment:P進大好きbot/What is the greatest ordinal notation now?/@comment-31966679-20180623154722/@comment-35470197-20180624220403

Really? I think that the definition is not fixed. In your blog post, \(lvl(x,y,z)\) is just defined for \(x > 0\), and hence \(lvl(0,0,0)\) is not defined, which is necessary for the definition of \(a_0(0)\).