User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190718022500/@comment-35470197-20190718045543

Good. Then it theoretically works if all of the theories are actually weaker than #60. (I do not know well about the comparison.) It does not mean the consistency strength, but the proof-theoretic strength.

Practically, there are several (non-serious) problems:
 * 1) We do not have an effective way to determine the level of a given explicit large number with respect to the ruler. (Analysis following the ruler is very difficult for the majourity of analysts here.)
 * 2) The base theory #60 is not the standard one, and hence googologists might not regard a large number well-defined in #60 as a valid computable googolism.
 * 3) For each level, there are few existing examples.