User blog comment:Lord Aspect/SATCLN V/@comment-35434595-20180713033735/@comment-4418057-20180713041414

Yep. ζ0^^ω is only ε(ζ0+1). ζ1 is εεεεεεε...ε(ζ0+1) with infinite epsilons.

A good rule of thumb is that to get to the next subordinal (ζ0, ζ1, ζ2, etc.), you have to do the same thing you did to make the nought ordinal in the first place.