Inaccessible limit of inaccessibles
= Inaccessible limit of inaccessibles
An <inaccessible cardinal> $\iota$ is an inaccessible limit of inaccessibles if the inaccessible cardinals below it are unbounded in $\iota$. A <rank cutoff at the first inaccessible limit of inaccessibles> shows that existence of unboundedly many inaccessibles does not prove existence of such a limit, provided the former theory is consistent.