User blog comment:Alemagno12/Huge Ordinal Analysis/@comment-30004975-20180203040658/@comment-25601061-20180203042102

I will post it when I make the blog post with the analysis, but, to summarize, we first define the set of all primes, and then define a well-ordering of non-negative integers of order type ωω by using multiplication and primes. We don't really have to prove that it is well-ordered, since I've found a way around that.