User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-24509095-20140509071457/@comment-24509095-20140510064142

Peng: Ohhh, I just realized that it's X(M). Everything makes sense now. :)

Ikosarakt: I wasn't really going to ask that but that looks very interesting. I was going to ask how in the world can one get from $$\chi(M)$$ to $$\chi(chi(...\chi(\chi(M)+1)...))$$? I'm not really sure. Since some cardinals have fundamental sequences, we know that the fundamental sequence of $$\psi_{\chi(M)_2}$$ contains $$\chi(\chi(M)+1)$$. Now, here's the problem, $$\psi_{\chi(\chi(M)+1)}$$ collapses to $$\chi(M)_{\chi(M)_{\chi(M)_{...}}}$$ which is definitely larger than $$\chi(M)_2$$. Btw, we've been thinking that things like $$\chi(M)_2$$ have fundamental sequences which they don't have. Just saying so as to not confuse Aarex. :P