User blog comment:Dchew89/An Ordinal Describing the Growth Rate of my d(n) Function/@comment-30754445-20190218043613

Unless you prescribe, exactly, how to choose the "larger ordinal" whenever we do a replacement, your concept is ill-defined. This means you need to:

(1) Name the exact fundamental sequences you're using.

(2) Prescribe how we choose the "larger ordinal" whenever there is more than one possible "larger ordinal" to choose from (for example, you could go from {1,ω} to ω^ω or to ε0)

This process, by the way, could give you as large an ordinal as you wish. You are not limited by ωck1 or even to countable ordinals. After all, there's nothing to stop us from saying that ω is the 2nd element in the fundamental sequence of any ordinal (larger or equal to ω*2) that we choose.