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- Title
ON CUTS IN ULTRAPRODUCTS OF LINEAR ORDERS II.
- Authors
GOLSHANI, MOHAMMAD; SHELAH, SAHARON
- Abstract
We continue our study of the class ${\cal C}\left( D \right)$ , where <italic>D</italic> is a uniform ultrafilter on a cardinal <italic>κ</italic> and ${\cal C}\left( D \right)$ is the class of all pairs $\left( {{\theta _1},{\theta _2}} \right)$ , where $\left( {{\theta _1},{\theta _2}} \right)$ is the cofinality of a cut in ${J^\kappa }/D$ and <italic>J</italic> is some ${\left( {{\theta _1} + {\theta _2}} \right)^ + }$ -saturated dense linear order. We give a combinatorial characterization of the class ${\cal C}\left( D \right)$. We also show that if $\left( {{\theta _1},{\theta _2}} \right) \in {\cal C}\left( D \right)$ and <italic>D</italic> is ${\aleph _1}$ -complete or ${\theta _1} + {\theta _2} > {2^\kappa }$ , then ${\theta _1} = {\theta _2}$.
- Subjects
LINEAR orderings; LARGE cardinals (Mathematics); ULTRAPRODUCTS; ULTRAFILTERS (Mathematics); NONSYMMETRIC matrices
- Publication
Journal of Symbolic Logic, 2018, Vol 83, Issue 1, p29
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2017.87