  In early 1979, Woodin extended this by showing that PD follows from much stronger large cardinal hypotheses. To describe this, let us introduce some terminology: Suppose j : Vλ+1 → Vλ+1 is a non-trivial elementary embedding. Let κ0(j) be the critical point of j and for each n let κn+1(j) = j(κn(j)). Let κw(j) ={sup}n&lt;ωκn(j). (Notice that j(κω(j)) = κω(j).)  A sequence of embeddings j0,…, jn is an n-fold strong rank to rank embedding sequence if there exists a λ such that 