On singular stationarity I (mutual stationarity and ideal-based methods)
نویسندگان
چکیده
منابع مشابه
On Singular Stationarity I (Mutual Stationarity and Ideal-Based methods)
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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For (κn)n<ω a strictly increasing sequence of regular cardinals > א2, Foreman and Magidor showed: if every sequence (Sn)n<ω of sets Sn, which are stationary in κn with ∀ξ ∈ Sn cof(ξ) = ω1, is mutually stationary then V 6= L. We show that the existence of a sequence (κn)n<ω with this property is equiconsistent with the existence of a measurable cardinal. In case (κn)n<ω=(אn+3)n<ω the property im...
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متن کاملA pr 2 00 1 More on mutual stationarity Preliminary
We prove that in the core model below 0 | • the following holds true. Let k ∈ OR \ 1. There is then a sequence (S i : i ∈ OR \ k, 0 < n < ω) such that • for all i ∈ OR \ k and n < ω \ 1 do we have that S i ⊂ אi+1 is stationary in אi+1 and α ∈ S n i ⇒ cf(α) = אk, and • for all limit ordinals λ and for all f :λ → ω \ 1 do we have that (S f(i) i : k ≤ i < λ) is mutually stationary if and only if t...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2019
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106790