User blog comment:Alemagno12/Huge Ordinal Analysis/@comment-11227630-20180203000827

Currently people have works on theory "KP + some ordinals". So here comes the question:

We say ordinal $$\alpha$$ (with some "large ordinal property") is "KP catch ZFC point" if the theory "KP + '$$\alpha$$ exists'" and "ZFC + '$$\alpha$$ exists'" have equal proof-theoretic ordinals. Then does KP catch ZFC point exist? If so, what's the least one?