ON SINGULAR STATIONARITY II (TIGHT STATIONARITY AND EXTENDERS-BASED METHODS)
نویسندگان
چکیده
منابع مشابه
On Singular Stationarity II (tight stationarity and extenders-based methods)
We study the notion of tightly stationary sets which was introduced by Foreman and Magidor in [8]. We obtain two consistency results which show that it is possible for a sequence of regular cardinals hnin<! to have the property that for every sequence ~ S, of some fixed-cofinality stationary sets Sn ✓ n, ~ S is tightly stationary in a generic extension. The results are obtained using variatio...
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We study several ideal-based constructions in the context of singular stationarity. By combining methods of strong ideals, supercompact embeddings, and Prikry-type posets, we obtain three consistency results concerning mutually stationary sets, and answer a question of Foreman and Magidor ([7]) concerning stationary sequences on the first uncountable cardinals, אn, 1 ≤ n < ω.
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Let κ be a singular cardinal of countable cofinality, 〈κn : n < ω〉 a sequence of regular cardinals which is increasing and cofinal in κ. Using a scale, we define a mapping μ from ∏ n P(κn) to P(κ+) which relates tight stationarity on κ to the usual notion of stationarity on κ+. We produce a model where all subsets of κ+ are in the range of μ for some κ a singular. Using a version of the diagona...
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We construct a model where every increasing ω-sequence of regular cardinals carries a mutually stationary sequence which is not tightly stationary, and show that this property is preserved under a class of Prikry-type forcings. Along the way, we give examples in the Cohen and Prikry models of ω-sequences of regular cardinals for which there is a non-tightly stationary sequence of stationary sub...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2019
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2018.46