Conjecture on CB ranks of Ziegler spectra of Prüfer domains

Let $R$ be a Prüfer domain and let $\lambda$ be a limit ordinal. The Ziegler-spectrum CB-rank conjecture. There does not exist a Prüfer domain whose Ziegler spectrum has Cantor–Bendixson rank $\lambda+1$. This conjecture concerns which ordinal ranks can occur for Ziegler spectra of Prüfer domains; the preceding results show that the CB rank is never equal to $1$, but the source gives no resolution of the asserted nonexistence for successor ordinals of the form $\lambda+1$ with $\lambda$ limit.