User blog comment:Googleaarex/Extended HyperNested Arrays/@comment-5150073-20130407201559/@comment-5150073-20130407205949

Nope. theta(e(W+2)) = theta(e(W+1)^e(W+1)^e(W+1)...e(W+1)^e(W+1)) (w times). Each increment to the epsilon's index creates power tower with w terms high, composed with previous ordinals. For instance:

e_1 = e_0^e_0^e_0...e_0^e_0^e_0 (w e_0's)

e_2 = e^1^e_1^e_1...e_1^e_1^e_1 (w e_1's)