User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-35470197-20180807012446

> Well, Deedlit also used the "I(ω) is the ωth inaccesible" version in his own post

Exactly...

> I'm guessing he used the definition-with-closure because it facilitated his proof.

To be more precise, I add that he just used \(I\) in his paper in order to explain relations among \(I\), \(\chi\), and \(Lambda_0\). What he actually used in his proof is \(\chi\). Therefore I know that \(I\) is not necessary for us.

> Unlike Rathjen, we can concentrate on making the notation as friendly to the user as possible.

So remembering what you said, i.e. Deedlit had already used the other \(I\), then I now agree with you...

Uh... it is personally very confusing for me, though...