User blog comment:Deedlit11/Ordinal Notations IV: Up to a weakly inaccessible cardinal/@comment-24509095-20140507175906/@comment-1605058-20140510065718

Iko: $$\vartheta$$ is useful. It is an injective function $$\varepsilon_{\Omega+1}\rightarrow\Omega$$ which, as Deedlit stated, "is convenient for some proofs". One can use it to, for example, directly show that cardinality of $$\varepsilon_{\Omega+1}$$ is the same as of $$\Omega$$.