Another important, and much stronger large cardinal notion is supercompactness. A cardinal \(\kappa\) is supercompact if for every \(\alpha\) there exists an elementary embedding \(j:V\to M\), with \(M\) transitive and critical point \(\kappa\), so that \(j(\kappa)&gt;\alpha\) and every sequence of elements of \(M\) of length \(\alpha\) belongs to \(M\).