On Fraïssé’s conjecture for linear orders of finite Hausdorff rank

We prove that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is φ2(0), the first fixed point of the ε-function. We then show that Fraïssé’s conjecture restricted to linear orders of finite Hausdorff rank is provable in  +“φ2(0) is well-ordered” and, over , implies  +“φ2(0) is well-ordered”.