User blog comment:Denis Maksudov/Fundamental sequences system for limit ordinals up to Large Veblen Ordinal/@comment-28606698-20170218162147

What do you think about next case: \theta(\Omega^{limit}*limit+limit, limit) ?

My suggestion:

Let $$\rho=\theta(\alpha+\Omega^{\delta}\cdot \xi + \beta, \gamma)$$

then


 * $$\rho[n]=\theta(\alpha+\Omega^{\delta}\cdot \xi + \beta, \gamma[n])$$ for any $$\delta$$, $$\xi$$, $$\beta$$ if $$\gamma$$ is a limit ordinal, $$\gamma< \rho$$,


 * $$\rho[n]=\theta(\alpha+\Omega^{\delta}\cdot \xi[n] + \beta, \gamma)$$ for any $$\delta$$, if $$\xi$$ is a limit ordinal and $$\beta$$, $$\gamma$$ are not a limit  ordinals,


 * $$\rho[n]=\theta(\alpha+\Omega^{\delta[n]}\cdot \xi + \beta, \gamma)$$ if $$\delta$$ is a limit ordinal and $$\xi$$, $$\beta$$, $$\gamma$$ are not a limit ordinals.