On cuts in ultraproducts of linear orders II

Abstract

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 $J^{\kappa }/D$ 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 $({\theta }_1,{\theta }_2)\in \mathcal{C}(D)$ and $D$ is ${\aleph }_1$-complete or ${\theta }_1+{\theta }_2>2^{\kappa },$ then ${\theta }_1={\theta }_2.$

arXiv commentThis is publication 1087 of second author