The saturation of club guessing ideals

Annals of Pure and Applied Logic 142 (1):398-424 (2006)
  Copy   BIBTEX

Abstract

We prove that it is consistent that there exists a saturated tail club guessing ideal on ω1 which is not a restriction of the non-stationary ideal. Two proofs are presented. The first one uses a new forcing axiom whose consistency can be proved from a supercompact cardinal. The resulting model can satisfy either CH or 20=2. The second one is a direct proof from a Woodin cardinal, which gives a witnessing model with CH

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2006.04.002

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,440

External links

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

Through your library

My notes

Similar books and articles

Some results about (+) proved by iterated forcing.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):515-531.
Club guessing sequences and filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.
ℙmax variations for separating club guessing principles.Tetsuya Ishiu & Paul B. Larson - 2012 - Journal of Symbolic Logic 77 (2):532-544.
A Tail Club Guessing Ideal Can Be Saturated without Being a Restriction of the Nonstationary Ideal.Tetsuya Ishiu - 2005 - Notre Dame Journal of Formal Logic 46 (3):327-333.
Club Guessing and the Universal Models.Mirna Džamonja - 2005 - Notre Dame Journal of Formal Logic 46 (3):283-300.
Aronszajn lines and the club filter.Justin Tatch Moore - 2008 - Journal of Symbolic Logic 73 (3):1029-1035.
Notes on Singular Cardinal Combinatorics.James Cummings - 2005 - Notre Dame Journal of Formal Logic 46 (3):251-282.
Weak saturation of ideals on Pκ(λ).Pierre Matet - 2011 - Mathematical Logic Quarterly 57 (2):149-165.
Club-guessing, stationary reflection, and coloring theorems.Todd Eisworth - 2010 - Annals of Pure and Applied Logic 161 (10):1216-1243.
James E. Baumgartner, Alan Taylor, and Stanley Wagon. Ideals on uncountable cardinals. Logic Colloquium '77, Proceedings of the colloquium held in WrocŁaw, August 1977, edited by Angus Macintyre, Leszek Pacholski, and Jeff Paris, Studies in logic and the foundations of mathematics, vol. 96, North-Holland Publishing Company, Amsterdam, New York, and Oxford, 1978, pp. 67–77. - J. E. Baumgartner, A. D. Taylor, and S. Wagon. Structural properties of ideals. Dissertationes mathematicae (Rozprawy matematyczne), no. 197, Polska Akademia Nauk, Instytut Matematyczny, Warsaw 1982, 95 pp. - James E. Baumgartner and Alan D. Taylor. Saturation properties of ideals in generic extensions. Transactions of the American Mathematical Society, vol. 270 (1982), pp. 557–574, and vol. 271 (1982), pp. 587–609. [REVIEW]Thomas Jech - 2001 - Bulletin of Symbolic Logic 7 (1):79-79.
A verification of the guessing-sequence hypothesis about spread of effect.C. A. Fagan & A. J. North - 1951 - Journal of Experimental Psychology 41 (5):349.
A saturation property of ideals and weakly compact cardinals.Joji Takahashi - 1986 - Journal of Symbolic Logic 51 (3):513-525.
Transfering saturation, the finite cover property, and stability.John T. Baldwin, Rami Grossberg & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (2):678-684.
The guessing-sequence hypothesis, the 'spread of effect' and number-guessing habits.William O. Jenkins & Leta M. Cunningham - 1949 - Journal of Experimental Psychology 39 (2):158.

Analytics

Added to PP
2013-12-31

Downloads
12 (#1,092,281)

6 months
3 (#984,658)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Nonexistence of universal orders in many cardinals.Menachem Kojman & Saharon Shelah - 1992 - Journal of Symbolic Logic 57 (3):875-891.
Club guessing sequences and filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.

View all 8 references / Add more references