User blog comment:QuasarBooster/Second-order worms ordinal analysis dump/@comment-36984051-20190620230843/@comment-35470197-20190621213857

You have ε_0+1 < ε_0+2 < ε_0+ε_0 < ε_0×ω = ω^(ε_0+1). Therefore ω^(…ω^(ε_0+2})…) just coincides with ω^(…ω^(ε_0+1})…).