User blog comment:Ubersketch/Collapsing the first 1-dinal/@comment-35470197-20190702215756/@comment-34422464-20190703002600

I don't see how being a proper class leads to ill-definedness. Sure, if you want to make this in ZFC you're going to have to make \(\overline{\Omega}\) be a pretty big ordinal, but I don't see the problem here.