User blog comment:Rgetar/Simple way to create lists of ordinals/@comment-37129238-20181007202038/@comment-32213734-20181008023956

Generally, true.

But the lists also depend on fundamental sequence system. If we take a different fundamental sequence system, that is different fundamental sequences for ordinals, then we can get different lists.

Also, we should throw away ζ0:

ω, ω + 1, ω2, ω2, ωω, ε0

So, a version of the double expansion of ω - ζ0 can be

ω, ω + 1, ω + 2, ω2, ω2 + 1, ω3, ω2, ω2 + 1, ω2 + ω, ω22, ω3, ωω, ωω + 1, ωω2, ωω + 1, ωω2, ωω 2, ωω ω , ε0, ε0 + 1, ε02, ωε0 + 1, ε1, εε 0

Then, the triple expansion of ω - ζ0 would be the collective single expansions of ω - ω + 1, ω + 1 - ω + 2, ω + 2 - ω2, ... , ωε0 + 1 - ε1, ε1 - εε 0, εε 0 - ζ0

etc.