User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-35392788-20180805073242

If you have an alternative definition I'll take it, but the C function is meant to go much, much further than just Mahlos. Keep in mind that I don't care in the slightest about power nor consistency with standard OCFs, I just want a formal version of UNOCF.

And yes, I am very conscious that UNOCF's Mahlos are weaker than standard OCF's (same for weakly compacts, especially for those), but it's not like it's the first time Username breaks tradition. I know that large cardinals above Mahlos get pretty weak in UNOCF. But accordingto Nish, the fact that it can be extended much MUCH further than most OCFs using the C function compensates for that.

iirc he said that Rathjen's K corresponded to UNOCF psi_T(T^T^T), but don't ask me anything about it.