User blog comment:KthulhuHimself/VAST function/@comment-1605058-20151124150523/@comment-2033667-20151128164044

You can do whatever you want in blogs, but that would be a bad idea for the mainspace.

What system would we use? I don't know of any published fundamental sequence system with a larger eta than the Wainer hierarchy. The Buchholz hierarchy is increasing, but it uses trees and not ordinals. Developing our own system would be extremely silly. As encyclopedists it is not up to us to define systems, but to record them.

By endorsing one fundamental sequence system as "correct," we imply that any other choice of FS system is incorrect. That's bad, because we want to encourage research in this field, including exploring alternative choices of FS systems.