In this talk we demonstrate that it is consistent that there is no linear order which is minimal with respect to being non $\sigma$-scattered.This shows a theorem of Laver, which asserts that the $\sigma$-scattered linear orders are well quasi-ordered is sharp. If time permits we will also prove that $\PFA^+$ implies that every non $\sigma$-scattered linear order either contains a real type, an Aronszajn type, or a ladder system indexed by a stationary set, equipped with either the lexicographic of reverse lexicographic order.