Consistency[]
ZFC+there exists a rank->rank cardinal IS consistent. Because:
- Rank->rank cardinals>N (the first \(\alpha\), that's \(\Pi_\alpha^\alpha\)-indescribable, also, Pi-ω+1-ω has an oracle axiom over Pi-ω-ω, generally, Pi-n+1-m has an oracle axiom over Pi-n-m, even if n or m is transfinite, and Pi-n-m is, with limit n, the supremum of Pi-k-m for all k<n.)
- N>K>M>I=\(\psi_I(0)>\omega_1\).
Strange how ZFC can't prove ψI(0)'s existence due to it being inaccessible!
Thus, if a rank->rank cardinal exists, so does N, K, M, I. QED 80.98.179.160 17:31, December 25, 2017 (UTC)
- It is not a proof, and the consistency is not known.
- p-adic 06:40, January 25, 2020 (UTC)
Separation into two or three arctiles[]
As L and V are useful hierarchy in both computable and uncomputable googology, I think that it is better to create articles on them. Do anyone have an opinion that we should include them into this artcle?
p-adic 06:40, January 25, 2020 (UTC)
If nobody disagrees with it, I will separate it into three articles.
p-adic 06:01, January 29, 2020 (UTC)
- Thank you. I wait a little for other opinions.
- p-adic 09:15, January 29, 2020 (UTC)
- Now I separated the article into three.
- p-adic 06:55, February 10, 2020 (UTC)