User blog comment:Hyp cos/General fundamental sequences for OCFs/@comment-28606698-20171005183657

1) As I understand your method allows to assign fundamental sequences only for countable limit ordinals.

2) Other examples for your general system:

2.1) For extended Buchholz's function fundamental sequences defined as follows;
 * $$C_0 = \{0\}$$,
 * $$C_{n+1} = \{\beta+\gamma,\psi_\mu(\eta)|\mu,\beta, \gamma,\eta\in C_n\}$$
 * $$L(\alpha)=\text{min}\{n<\omega|\alpha\in C_n\}$$
 * $$\alpha[n]=\text{max}\{\beta<\alpha|L(\beta)\le L(\alpha)+n\}$$

2.2) For the function collapsing weakly Mahlos cardinals fundamental sequences defined as follows: where $$R$$ denotes set of all uncountable regular cardinals and $$W$$ denotes set of all weakly Mahlos cardinals.
 * $$C_0= \{0\}$$
 * $$C_{n+1}= \{\alpha+\beta,M_\gamma,\chi_\delta(\epsilon),\psi_\zeta(\eta)|\alpha,\beta,\gamma,\delta,\epsilon,\zeta,\eta\in C_n\wedge\delta\in W\wedge\zeta\in R\}$$
 * $$L(\alpha)=\text{min}\{n<\omega|\alpha\in C_n\}$$
 * $$\alpha[n]=\text{max}\{\beta<\alpha|L(\beta)\le L(\alpha)+n\}$$

If you find those examples are correct, I'll add them as well as your own example to the List of systems of fundamental sequences.