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- W2078955917 abstract "Abstract This paper investigates when it is possible for a partial ordering ℙ to force P k (Λ)V to be stationary in V ℙ . It follows from a result of Gitik that whenever ℙ adds a new real, then P k (Λ)V is stationary in V ℙ for each regular uncountable cardinal κ in V ℙ and all cardinals λ ≥ κ in V ℙ [4], However, a covering theorem of Magidor implies that when no new ω-sequences are added, large cardinals become necessary [7]. The following is equiconsistent with a proper class of ω 1 -Erdős cardinals: If ℙ is ℵ 1 -Cohen forcing, then P k (Λ)V is stationary in V ℙ , for all regular κ ≥ ℵ 2 and all λ ≩ κ. The following is equiconsistent with an ω 1 -Erdős cardinal: If ℙ is ℵ 1 -Cohen forcing, then is stationary in V ℙ . The following is equiconsistent with κ measurable cardinals: If ℙ is κ-Cohen forcing, then is stationary in V ℙ ." @default.
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- W2078955917 date "2006-09-01" @default.
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- W2078955917 title "Co-stationarity of the ground model" @default.
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- W2078955917 doi "https://doi.org/10.2178/jsl/1154698589" @default.
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