On Fraïssé's conjecture for linear orders of finite Hausdorff rank
The paper proves that the maximal order type of the wqo of linear orders of finite Hausdorff rank under embeddability is \(\phi_2(0)\), the first fixed point of the \(\varepsilon\)-function. Moreover, it proves that Fraïssé's conjecture restricted to linear orders of finite Hausdorff rank is provable in \(\text{ACA}^+_0\) + ``\(\varphi_2(0)\) is well-ordered'' and, over \(\text{RCA}^+_0\), implies \(\text{ACA}'_0\) + ``\(\varphi_2(0)\) is well-ordered''.
scientific article; zbMATH DE number 5620643
scientific article