User blog comment:B1mb0w/Fundamental Sequences/@comment-5529393-20151113121456/@comment-10262436-20151115023522

I have edited the Alternative Rule Set to generalise better. It should now address every example you gave where a limit ordinal is present.

Returning to the diagonal of [0] formulas. You say the alternative rule set produces similar results and that may or may not be correct. However, in all my practical calculations, I have no need to calculate phi(mu)[0] etc. It does not come up. The diagonal of [1] will always collapse to omega. The diagonals of [2] and [3] produce interesting results.

Therefore my original comment is that I find the usual rule set more complicated than I would expect because it relies on decrementing the diagonal [n] and being forced to define the diagonal of [0] with artificial or non unique rules.