User blog comment:TheKing44/Ordinal Definable System of Fundamental Sequences/@comment-35470197-20191201030851/@comment-35470197-20191203113857

I have another question. Is there a specific way to choose a large ordinal below ω_1^{HOD}? Unlike ω_1^{CK}, it can be uncountable, and hence it looks a non-trivial question.

I also created a large function based on the definability at von Neumann hierarchy in ZFC set theory here, and am interested in whether your system can yield a greater function. I would like you to give me an opinion.