User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180129200050/@comment-30118230-20180129204605

Well,I don't think there is a stronger recursive ordinal notation stronger than Taranovsky's.

I don't know how much you know about TON,but Taranovsky has proposed that the n=2 system is already significantly stronger than SOA or even ZFC,so there is that.

"Raw strength" is a very subjective term,especially in googology and ordinal analysis,but like you said,most people would agree that Taranovsky's is a ridiculously strong one.