Co-stationarity of the Ground Model

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

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Full reflection at a measurable cardinal.Thomas Jech & Jiří Witzany - 1994 - Journal of Symbolic Logic 59 (2):615-630.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Ad and patterns of singular cardinals below θ.Arthur W. Apter - 1996 - Journal of Symbolic Logic 61 (1):225-235.
Proper forcing and remarkable cardinals II.Ralf-Dieter Schindler - 2001 - Journal of Symbolic Logic 66 (3):1481-1492.
Large cardinals and large dilators.Andy Lewis - 1998 - Journal of Symbolic Logic 63 (4):1496-1510.
Proper forcing and l(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
Unfoldable cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
Jónsson cardinals, erdös cardinals, and the core model.W. J. Mitchell - 1999 - Journal of Symbolic Logic 64 (3):1065-1086.
Some structural results concerning supercompact cardinals.Arthur W. Apter - 2001 - Journal of Symbolic Logic 66 (4):1919-1927.

Analytics

Added to PP
2010-08-24

Downloads
26 (#596,950)

6 months
8 (#347,798)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

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.
2007 Annual Meeting of the Association for Symbolic Logic.Mirna Džamonja - 2007 - Bulletin of Symbolic Logic 13 (3):386-408.

Add more citations

References found in this work

On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
On the size of closed unbounded sets.James E. Baumgartner - 1991 - Annals of Pure and Applied Logic 54 (3):195-227.
Minimal collapsing extensions of models of zfc.Lev Bukovský & Eva Copláková-Hartová - 1990 - Annals of Pure and Applied Logic 46 (3):265-298.
Some applications of short core models.Peter Koepke - 1988 - Annals of Pure and Applied Logic 37 (2):179-204.
Forcing with trees and order definability.Thomas J. Jech - 1975 - Annals of Mathematical Logic 7 (4):387.

Add more references