User blog comment:Ikosarakt1/Coding strings as ordinals (for Friedman's n(k))/@comment-5529393-20130715142426/@comment-1605058-20130715153259

In your well-order definition, BA has same ordinal as A. I think all such equivalences can be prevented by replacing a*w^k for largest k with (a+1)*w^k. I also am interested in how n(k+4)>F(k) bound was achieved, I might try to discover it by myself.