Co-stationarity of the ground model

Dobrinen, Natasha; Friedman, Sy-David

J. Symbolic Logic, Tome 71 (2006) no. 1, p. 1029-1043 / Harvested from Project Euclid

Résumé

This paper investigates when it is possible for a partial ordering ℛ to force 𝒫_κ(λ)∖ V to be stationary in V^ℛ. It follows from a result of Gitik that whenever ℛ adds a new real, then 𝒫_κ(λ)∖ V is stationary in V^ℛ for each regular uncountable cardinal κ in V^ℛ and all cardinals λ>κ in V^ℛ [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 ℛ is ℵ₁-Cohen forcing, then 𝒫_κ(λ)∖ V is stationary in V^ℛ, for all regular κ≥ℵ₂ and all λ>κ. The following is equiconsistent with an ω₁-Erdős cardinal: If ℛ is ℵ₁-Cohen forcing, then 𝒫_ℵ₂(ℵ₃)∖ V is stationary in V^ℛ. The following is equiconsistent with κ measurable cardinals: If ℛ is κ-Cohen forcing, then 𝒫_κ⁺(ℵ_κ)∖ V is stationary in V^ℛ.

Publié le : 2006-09-14
Classification: 𝒫_κ λ, co-stationarity, Erdös cardinal, measurable cardinal, 03E35, 03E45

@article{1154698589,
     author = {Dobrinen, Natasha and Friedman, Sy-David},
     title = {Co-stationarity of the ground model},
     journal = {J. Symbolic Logic},
     volume = {71},
     number = {1},
     year = {2006},
     pages = { 1029-1043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1154698589}
}

Dobrinen, Natasha; Friedman, Sy-David. Co-stationarity of the ground model. J. Symbolic Logic, Tome 71 (2006) no. 1, pp.  1029-1043. http://gdmltest.u-ga.fr/item/1154698589/