FPT 2

Since my last definiton was evidently trash, I made a new and simpler version, f_v(L) |-> (O |-> O):

https://testitem.github.io/colg/fpt3.html

1. \(f_0(0) = \alpha \mapsto \varepsilon_\alpha\)
2. \(f_L(0) = \alpha \mapsto \alpha @f_{L-1}(\ddots)\) when L is a successor ordinal
3. \(f_L(0) = \alpha \mapsto \sup\{f_r(0)(\alpha):r<L\}\) when L is a limit ordinal
4. \(f_L(v) = \alpha \mapsto \alpha @f_L(v-1)\)
5. \(f_L(\ddots) = \alpha \mapsto 0 @f_L(\alpha)\)
6. \(r(L) = f_L(\ddots)(0)\)
7. \(t=\sup\{v<\omega:r(v)\}\) and \(T=0@r\)

What are t and T, relative to other ordinals?