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On cuts in ultraproducts of linear orders I

2016
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Journal of Mathematical Logic
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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 . 3 In fact it is easily seen that κ * = θ 1 . M. GOLSHANI AND S. SHELAH Proof. Suppose not. Let J be a θ + −saturated dense linear order and suppose f α /D : α < θ , g α /D : α < θ witnesses (θ, θ) ∈ C (D). For α < β < θ we have Since 2 κ < θ

doi:10.1142/s0219061316500082
fatcat:osc373z3rvcbznrzvz6swu2o7q