User blog comment:PsiCubed2/My attempt for creating an ψ(ψᵢ(0))-level notation for ordinals/@comment-24920136-20170329070238/@comment-30754445-20170403205553

Even with your stronger definition, +-0-1 doesn't seem to correspond to ε₀,

According to Buchholz own definition (with the subtree copied only once), +-0-1 expands to the simple Kirby-Paris Hydra +0-0-0 (which corresponds to ωω)

Copying the subtree n times would still be a Kirby-Paris Hydra of the same depth only with n branches instead of one. This corresponds to the ordinal ωω×n, which gives us a limit of ωω².

Could you have mis-remembered which tree corresponds to which ordinal? Maybe it is required to stick an "ω"-labeled node somewhere to go beyond ε₀?

Well, the good news is that the above analysis confirms that the "replicating the tree n times" bit doesn't change the final results by much. It's equivalent to a mere multiplication by ω.