Co-stationarity of the Ground Model

Journal of Symbolic Logic 71 (3):1029 - 1043 (2006)

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Abstract
This paper investigates when it is possible for a partial ordering P to force Pκ(λ) \ V to be stationary in VP. It follows from a result of Gitik that whenever P adds a new real, then Pκ(λ) \ V is stationary in VP for each regular uncountable cardinal κ in VP and all cardinals λ > κ in VP [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 ω₁-Erdős cardinals: If P is N₁-Cohen forcing, then Pκ(λ) \ V is stationary in VP, for all regular κ ≥ N₂ and all λ > κ. The following is equiconsistent with an ω₁-Erdős cardinal: If P is N₁-Cohen forcing, then PN₂ (N₃) \ V is stationary in VP. The following is equiconsistent with κ measurable cardinals: If P is κ-Cohen forcing, then Pκ + (Nκ \ V is stationary in VP
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DOI 10.2178/jsl/1154698589
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References found in this work BETA

On the Size of Closed Unbounded Sets.James E. Baumgartner - 1991 - Annals of Pure and Applied Logic 54 (3):195-227.
Some Applications of Short Core Models.Peter Koepke - 1988 - Annals of Pure and Applied Logic 37 (2):179-204.
Minimal Collapsing Extensions of Models of Zfc.Lev Bukovský & Eva Copláková-Hartová - 1990 - Annals of Pure and Applied Logic 46 (3):265-298.
Forcing with Trees and Ordinal Definability.Thomas J. Jech - 1975 - Annals of Mathematical Logic 7 (4):387-409.

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Citations of this work BETA

Internal Consistency and the Inner Model Hypothesis.Sy-David Friedman - 2006 - Bulletin of Symbolic Logic 12 (4):591-600.
Some Applications of Mixed Support Iterations.John Krueger - 2009 - Annals of Pure and Applied Logic 158 (1-2):40-57.

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