User blog comment:ArtismScrub/Generalization of chained arrow notation/@comment-30118230-20180217152738

Indeed,the limit of this extention is $$\omega^{\omega^\omega}$$ though I don't quite know how you got the idea for $$\varepsilon_0$$. Also,you don't just need to give examples,but actual definitions,which could be applied in every possible case for the notation.