User blog comment:Ubersketch/What are some ways to map a well-order to the natural numbers without using a Godel coding/@comment-39541634-20190909210146/@comment-34422464-20190910201452

My original idea was to get something similar to this mapping from CNF to the natural numbers:

Let e0[n]=w^^n

To generate the sequence:

The sequence is started by e0

Take the sequence you currently have S and create a new sequence of all limit ordinals in the current sequence in order, call this sequence L. For all ordinals a in L, replace it with a[n] such that n is the minimum n such that a[n] is not in S. Append to S.

I don't think this works if you just have a well-order though. I'd like other examples as well.