Talk:Rank-into-rank cardinal

ZFC+there exists a rank->rank cardinal IS consistent. Because:
 * 1) Rank->rank cardinals>N (the first \(\alpha\), that is \(\Pi_\alpha^\alpha\)-indescribable, also, Pi-ω-(ω+1) has an oracle axiom over Pi-ω-ω, generally, Pi-n-(m+1) has an oracle axiom over Pi-n-m, even if n or m is transfinite, and Pi-n-m is, with limit m, the supremum of Pi-n-k for all kK>M>I>\(\psi_I(0)>\omega_1\).

Thus, if a rank->rank cardinal exists, so does N, K, M, I. QED