User blog comment:Deedlit11/Ordinal Notations III: Collapsing Higher Cardinalities/@comment-7484840-20130706154845/@comment-7484840-20130706185155

I can see what your saying: the theta function uses gamma because it does not have the types on the theta itself (no theta_n), and so cannot do the things that the psi function can do with nesting like alpha |-> psi_2(alpha), so it just has to use the gamma instead. Surely though, this has problems with larger ordinals, for example,  what would the theta equivalent of $$\alpha\mapsto\psi_3(\Omega^{\alpha})$$ be?