User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-35470197-20180806230450

Exactly. As I wrote another comment above, there are two conventions, which are both commnly used. I just meant that it conflicts the convention in Rathjen's OCF. I mind it just because Rathjen's OCF is the origin of Deedlit's OCF.

Anyway, do you know the reference of What Deedlit wrote?: \(ψ_{Ω_1}(\varepsilon_{M+1})\) is the proof theoretic ordinal of \(\textrm{KP) + "There exists a recursively Mahlo ordinal".

I am looking for a reference of this fact for Deedlit's or Rathejen's OCF. The same equality (maybe for Rathjen's OCF?) is written in an article in this wiki by Fluoroantimonic Acid, but I do not know a reference. I asked Fluoroantimonic Acid, but there is no answer. I am also asking Emlightened, who stated that this equality holds for Rathjen's OCF.

I note that it is written in Rathjen's paper that the proof-theoretic ordinal is equal to \(\psi_{\Omega_1}(\psi_{\chi_{\varepsilon_{M+1}(0)}(0))\), which looks different from \(ψ_{Ω_1}(\varepsilon_{M+1})\), because the cofinality of \(\varepsilon_{M+1}\) is \(\omega\).