User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180805015451/@comment-35470197-20180806220902

@PsiCubed2

> I'm not sure why Deedlit didn't simply used I(a,b) (or Ia,b) instead of χ(a,b).

Isn't that simply because \(I\) is not enumerating weakly inaccessibles unlike \(\chi\)? If you remember the proof of the well-definedness of Rathjen's OCF, you need to ensure that the values of \(\chi\) does not appear standard expressions of \(\phi\) and \(\Phi\). It holds because every value of \(\chi\) is weakly inaccessible, but if you use \(I\), which is defined as the enumeration of the closure of the classes of higher weakly inaccessibles so that it is Scott coontinuous separatedly on each variable. Since the regularity is not closed with respect to Scott topology, such a difference always occurs when we consider any large cardinals.