User blog comment:QuasarBooster/Second-order worms ordinal analysis dump/@comment-36984051-20190620230843/@comment-35470197-20190621012701

Although I do not clearly understand the meaning of the question, ε_α for a limit ordinal α is given as the supremum of the set of {ε_β|β<α}. In particular, when　α is a countable limit ordinal with a fundamental sequence α[n], ε_α is the limit of ε_(α[n]).

For example, you can compute ε_(ζ_0*2) as the limit ε_(ζ_0+φ(1,φ(1,…φ(1,0)…))), and ε_(ζ_0^2) as the limit ε_(ζ_0×φ(1,φ(1,…φ(1,0)…))).