On cuts in ultraproducts of linear orders I

For an ultrafilter $D$ on a cardinal $κ,$ we wonder for which pair $(θ_1, θ_2)$ of regular cardinals, we have: for any $(θ_1+θ_2)^+-$saturated dense linear order $J, J^κ/ D$ has a cut of cofinality $(θ_1, θ_2).$ We deal mainly with the case $θ_1, θ_2 > 2^κ.$

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