User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-5529393-20170402194355

There are still many expressions missing from your definition involving \(\Omega\).

For example, any expression ending in \(\Omega \alpha\) where \(\alpha\) is a countable ordinal.

Also, it looks like the only expressions involving exponents that you handle are ones that end in \(\Omega^{\Omega^{\cdots^\Omega}}\), but most expressions do not. In general, we have something like \(\Omega^{\alpha_1} \beta_1 + \ldots + \Omega^{\alpha_n}\), where \(\alpha_n = \Omega^{\gamma_1} \delta_1 + \ldots + \Omega^{\gamma_m}\), where \(\gamma_m = \(\Omega^{\epsilon_1} \eta_1 + \ldots + \Omega^{\epsilon_p}\), and so on.