User blog comment:Deedlit11/Ordinal Notations IV: Up to a weakly inaccessible cardinal/@comment-24509095-20140507175906/@comment-5150073-20140510061711

$$\vartheta$$ isn't useful because we have to write extra rules for 2-nd argument (as it is binary) without boosting the strength of notation. By the same reason I prefer Hardy hierarchy instead of FGH.