User blog comment:Hyp cos/General fundamental sequences for OCFs/@comment-28606698-20171002182439

In april when I was studying Buchholz's function I was having similar idea:
 * $$C_\nu^0(\alpha) = \{\beta|\beta<\Omega_\nu\}$$,
 * $$C_\nu^{n+1}(\alpha) = \{\beta+\gamma,\psi_\mu(\eta)|\mu,\beta, \gamma,\eta\in C_{\nu}^n(\alpha)\wedge\eta<\alpha\}$$,
 * $$C_\nu(\alpha) = \bigcup_{n < \omega} C_\nu^n (\alpha)$$,
 * $$\psi_\nu(\alpha) = \min\{\gamma | \gamma \not\in C_\nu(\alpha)\}$$,

and

$$\psi_\nu(\alpha)[n]=\text{max}\{\beta<\alpha|\beta\in C_{\nu}^n(\alpha)\}$$.

although - yes - addition creates some problem, but nevertheless we can plug those fundamental sequences to the fast-growing hierarchy (but it gives another results in comparing with the case of using of standard system of FS).