User blog comment:Ecl1psed276/BM2 Analysis - A Summary/@comment-30754445-20180709051740/@comment-32697988-20180712045511

@PsiCubed2

He did say that C(1;0;0) is K, but he did not say that C(1;0;0) corresponds to a weakly compact cardinal in standard OCF (like Deedlit's OCF) or Pi-3 reflecting ordinal. Username is talking about UNOCF, which is a OCF that does not require knowledge of set theory (for example, knowing the definition of Mahlo cardinal) unlike other OCFs like Deedlit's OCF or Rathjen's OCF. And the "analysis" shown in this blog is also in UNOCF as well. C(1;0;0) in UNOCF is defined to be K in UNOCF.

It is true that UNOCF is not defined formally but it is easier to understand than other OCFs. However, K in UNOCF does not necessarily corresponds to K in other OCFs. And according to what people say on discord, K in UNOCF is actually weaker than K in other OCFs, although this is not proven formally yet. This means K here does not have to be Pi-3 reflecting ordinal. In UNOCF things like I, M, and K are not treated as inaccessible, Malho and compact cardinals, but rather some symbol that can be used in psi function, which is why UNOCF does not require knowledge of set theory.

Lastly, you mentioned doing a survey to people asking what recursive ordinals they are comfortable working with in yout last comment, but I cannot find the survey here. Can you give us a link to the survey result or someting similar?