User blog comment:DrCeasium/HAN: better definitions/@comment-25418284-20130609194217

Warning: \(\theta(\alpha \mapsto \Omega_\alpha)\) is just \(\theta(\varepsilon_{\Omega + 1})\). The theta function becomes constant at the Bachmann-Howard ordinal. What you want is a variant of the theta function that goes up to \(\alpha \mapsto \Omega_\alpha\).

I think I can define it: \(\lambda(\alpha)\) is the smallest ordinal that cannot be expressed using \(0,1,\omega\), sums, products, exponentials, the function \(\alpha \mapsto \Omega_\alpha\), and the \(\lambda\) function itself.