On cuts in ultraproducts of linear orders II

We continue our study of the class $\mathcal{C}(D)$, where $D$ is a uniform ultrafilter on a cardinal $\kappa$ and $\mathcal{C}(D)$ is the class of all pairs $({\theta }_1,{\theta }_2),$ where $({\theta }_1,{\theta }_2)$ is the cofinality of a cut in $J^{\kappa }\mathrm{/}D$ and $J$ is some $({\theta }_1+{\theta }_2{)}^{+}$-saturated dense linear order. We give a combinatorial characterization of the class $\mathcal{C}(D)$. We also show that if $(\theta_1, \theta_2) \in \mathscr{C}(D)$and$D$is$\aleph_1$-completeor$\theta_1 + \theta_2 > 2^\kappa,$then$\theta_1=\theta_2.$