User blog comment:KthulhuHimself/Norminals Revisited./@comment-27173506-20160204132906/@comment-27173506-20160204192500

Ah, I see where my mistake is: <0,a> is defined merely as the supremum of {<0,a-1>,<<0,a-1>,a-1>,<<<0,a-1>,a-1>,a-1>...}, and not as a new limit to what we can construct with <0,a-1>. If so, then this is definitely far weaker than Ord2. I believe we'd have <0,a>=\(\text{Ord}\w^a-1\), <0,0,1>=\(\text{Ord}^2\) and \(\text{sup} \lbrace <0,1>, <0,0,1> , <0,0,0,1> ... \rbrace = \phi(\w,\text{Ord}+1)\). Not bothering to prove now, just saying an assumption.