User blog comment:PsiCubed2/My attempt for creating an ψ(ψᵢ(0))-level notation for ordinals/@comment-24920136-20170329070238/@comment-5529393-20170403231343

Sorry, by "replicate the subtree n times" I meant the following:

The normal rule for reducing a leaf U with a positive label n is as follows:  We go up the tree until we reach a vertex V with label less than n, then we create a tree T' that is identical to the subtree starting from U, except we replace the label for the root (call it U') with n-1, and the label for the vertex corresponding to V (call it V') with 0. Then we replace V with T'.

What I meant was that we replace V with T', then replace V' with T', then the V' from that tree with T', and so on until we have done the replacement n times.

So +-0-1 will be +-0-0-0...-0 with n copies of 0, so it will indeed be a sequence of trees with order types whose supremum is \(\varepsilon_0\).