The nonstationary ideal on ℵ2
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We construct a model in which the filter of ω-closed unbounded subsets of ℵ2 is precipitous and a model in which the filter of closed unbounded subsets of ℵ2 is precipitous. For the first model we need a measurable cardinal, and for the second a measurable cardinal of order 2. Both results are equiconsistent.
KeywordsDense Subset Generic Subset Measurable Cardinal Force Notion Elementary Chain
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