User blog comment:Ecl1psed276/Question about standard notation/@comment-30754445-20180808072912/@comment-25601061-20180808124432

i honestly don't see how having Iω = ωth inaccessible makes things easier to understand - not only does it make things more confusing for learners, but it's also inconsistent and makes the notation uglier

in fact during all the time i've known about the inaccessible ocf i thought Iω was the limit of In for finite n and not the ωth inaccessible

imo Iω = ωth inaccessible because the creator of the OCF (rathjen?) wanted to make it like that for some reason (or was it adapted from jäger's OCF?)