User blog comment:Deedlit11/Ordinal Notations VI: Up to a weakly compact cardinal/@comment-5150073-20140515153351

If I got this correctly, we suppose that we can extend index of Mahlo to linear function so that, for example, $$M(\alpha) = M_\alpha$$ and $$M(1,0) = M_{M_{M_{M_{\cdots}}}}$$, all the way up to $$M(\alpha_1,\alpha_2,\cdots,\alpha_m)$$ and then turn it to some principically new $$\Psi_{\Xi(1)}$$ function as $$\Psi_{\Xi(1)}(\Xi(1)^{\alpha_1}+\Xi(1)^{\alpha_2}+\cdots+\Xi(1)^{\alpha_m})$$. Then $$\Xi(1)$$ must be extended in the way which we extended Mahlo just now, and generally $$\Xi(\alpha+1)$$ is the diagonalizer of $$\psi_{\Xi(\alpha+1)}$$, which indicates $$\Xi(\alpha)(\alpha_1,\alpha_2,\cdots,\alpha_m)$$ function. "K"-diagonalizer is a diagonalizer of $$\Xi(\alpha)$$ function itself. It may be stronger than I think, and D(0) in my notation won't reach it. Ikosarakt1 (talk ^ contribs) 15:33, May 15, 2014 (UTC)