User blog comment:Nayuta Ito/faketest/e0/@comment-35470197-20180806011007

What is the definition of \(I_{I_{I_{\cdot_{\cdot_{\cdot}}}}}\) in the table?

If we regard \(I\) just as a formal function symbol, it does not make sense.

If we define \(I\) in set theory, then it is ok. In this case, does \(I_{\alpha}\) mean the \(\alpha\)-th weakly inaccessible, or the \(\alpha\)-th ordinal in the closure of the class of weakly inaccessibles? We often use both conventions, but the result of \(I_{I_{I_{\cdot_{\cdot_{\cdot}}}}}\) depends on the choice of conventions. (For example, \(I_{\omega}\) is weakly inaccesible in the first convention, but is not in the second convention.)