User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-7484840-20130620190007/@comment-5529393-20130620215435

The second and third rules don't work, as I have been talking about with Ikosarakt1. The theta rules you are using will lead to a weaker notation than the proper rules, and there are issues such as taking \(\Omega [n]\) and not having rules for ordinals that are more than 1 larger than a limit ordinal.