Given a positive integer \(n\), an \(n\)-ladder is a lower finite lattice in which every element has at most \(n\) lower covers. In 1984, Ditor proved that every \(n\)-ladder has cardinality at most \(\aleph_{n-1}\) and asked whether this bound is sharp, i.e., whether for each \(n > 0\) there exists an \(n\)-ladder of cardinality \(\aleph_{n-1}\). We survey known results on this problem and some more recent developments.
