On the number of cofinalities of cuts in ultraproducts of linear orders

Abstract

Suppose $\kappa$ is a regular cardinal and $\bar{a}=⟨{\mu }_i:i<\kappa ⟩$ is a non-decreasing sequence of regular cardinals. We study the set of possible cofinalities of cuts Pcut$(\bar{a})=\{({\lambda }_1,{\lambda }_2):$ for some ultrafilter $D$ on $\kappa$, $({\lambda }_1,{\lambda }_2)$ is the cofinality of a cut of $\prod _{i<\kappa }{\mu }_i/D\}$.

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