For example, there are reflection principles that imply the existence of and I3 rank-into-rank cardinals, which are among the cardinals with greatest consistency strength whose existence is believed to be consistent with ZFC.
There are reflection principles. This is for example. These reflection principles imply the existence of and I3 rank-into-rank cardinals. Rank cardinals are among the cardinals with greatest consistency strength. Greatest consistency strength's existence is believed to be consistent with ZFC.