On cuts in ultraproducts of linear orders I

Abstract

For an ultrafilter $D$ on a cardinal $\kappa ,$ we wonder for which pair $({\theta }_1,{\theta }_2)$ of regular cardinals, we have: for any $({\theta }_1+{\theta }_2{)}^{+}-$saturated dense linear order $J,J^{\kappa }/D$ has a cut of cofinality $({\theta }_1,{\theta }_2).$ We deal mainly with the case ${\theta }_1,{\theta }_2>2^{\kappa }.$

arXiv commentThis is publication 1075 of second author