User blog comment:Ecl1psed276/Question about standard notation/@comment-30754445-20180808072912/@comment-35470197-20180808132043

@Alemagno12

> 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

I guess that it might cause troubles when you compute values of Rathjen's OCFs, because the weak inaccessibility of the values of I's is strictly used in the definitions of them. Maybe I think that you are not just regarding I_w as a shorthand of the limit of I_n's, but are also simultaneously regarding F(I_w) as a shorthand of the limit of F(I_n)'s for several function symbols F. (If you only regard I_w as the limit of I_n, then F(I_w) does not necessarily coincides with the limit of F(I_n). Then you might feel confused by the inconnsistency of the notation.)

> 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?)

At least, Rathjen did not in those papers. He denoted by I_a(b) the b-th ordinal in the closure of the class of weakly a-inaccessible cardinal, and by chi_a(b) the b-th weakly a-inaccessible cardinal. So I_w is just a function there.