The last post was not good; but, at least, it teached me to clear everything up before going forward (and other users told me that too :P).
You can check Wythagoras' definition here!
The analysis is at Wythagoras' blog post.
If is a successor ordinal,
If is a limit ordinal,
Darn. I'm extremely confused about this.
THIS WORK IS NOT IN PROGRESS ANYMORE BECAUSE OF EXTREME CONFUSION.