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

Abstract

Suppose $\kappa$ is a regular cardinal and $\bar a=\langle \mu_i: i<\kappa \rangle$ 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 $\prod\limits_{i<\kappa} \mu_i / D \}$.