User blog comment:Ubersketch/A proposal for a standard/@comment-35470197-20190811012241/@comment-35392788-20190812071041

I personally use Buchholz's OCF up to the TFB, and after that I would be interested in learning about Rathjen's weakly Mahlo or weakly compact OCF. However, these OCFs seem complex, so maybe we need an intermediate OCF, which would go to the countable collapse of the first omega-fixed point.