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IPM
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“School of Mathematics”

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Paper   IPM / M / 16083
School of Mathematics
  Title:   On cuts in ultraproducts of linear orders II
  Author(s):  Mohammad Golshani (Joint with S. Shelah)
  Status:   Published
  Journal: J. Symbolic Logic
  Vol.:  83
  Year:  2018
  Pages:   29-39
  Supported by:  IPM
  Abstract:
We continue our study of the class \mathscrC(D), where D is a uniform ultrafilter on a cardinal κ and \mathscrC(D) is the class of all pairs (θ1, θ2), where (θ1, θ2) is the cofinality of a cut in J\k/D and J is some (θ12)+-saturated dense linear order. We give a combinatorial characterization of the class \mathscrC(D). We also show that if (θ1, θ2) ∈ \mathscrC(D) and D is ℵ1-complete or θ1 + θ2 > 2κ, then θ12.

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