User blog comment:KthulhuHimself/Norminals Revisited./@comment-5529393-20160710171207

Kthulhu, in the definition of N_<0,2>, you quantify over any ordinal a or any  value. So if we define T_0 = <0,1>, and T_{n+1} = , then the union of the T_n is closed under your rules; if a is in the union of T_n, then a belongs to T_n for some n, so  belongs to T_{n+1}, and therefore the union of the T_n. So we do in fact get that N_<0,2> is the limit of N_<...<0,1>,1>,...,1>.