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 \varphi_2(0), the first fixed point of the \epsilon-function. We then show that Fraïssé's conjecture restricted to linear orders of finite Hausdorff rank is provable in ACA_0^+ + "\varphi_2(0) is well-ordered" and, over RCA_0, implies ACA_0' + "\varphi_2(0) is well-ordered".