Annals of Pure and Applied Logic 149 (1-3):100-123 (2007)

Starting with a λ-supercompact cardinal κ, where λ is a regular cardinal greater than or equal to κ, we produce a model with a stationary subset S of such that , the ideal generated by the non-stationary ideal over together with , is λ+-saturated. Using this model we prove the consistency of the existence of such a stationary set together with the Generalized Continuum Hypothesis . We also show that in our model we can make -saturated, where S is the set of all such that , the order type of x, is a regular cardinal and x is stationary in sup. Furthermore we construct a model where is κ+-saturated but GCH fails. We show that if SS is stationary in , then S can be split into λ many disjoint stationary subsets
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2007.08.002
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,316
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
On Strong Compactness and Supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.

View all 9 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Splitting Stationary Sets In.Toshimichi Usuba - 2012 - Journal of Symbolic Logic 77 (1):49-62.
A Relative of the Approachability Ideal, Diamond and Non-Saturation.Assaf Rinot - 2010 - Journal of Symbolic Logic 75 (3):1035-1065.
Saturation, Suslin Trees and Meager Sets.Paul Larson - 2005 - Archive for Mathematical Logic 44 (5):581-595.
Orders of Indescribable Sets.Alex Hellsten - 2006 - Archive for Mathematical Logic 45 (6):705-714.
Splitting $P_kappalambda$ Into Stationary Subsets.Yo Matsubara - 1988 - Journal of Symbolic Logic 53 (2):385-389.
Stationary Cardinals.Wenzhi Sun - 1993 - Archive for Mathematical Logic 32 (6):429-442.
Reflecting Stationary Sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.


Added to PP index

Total views
5 ( #1,207,698 of 2,519,443 )

Recent downloads (6 months)
1 ( #407,861 of 2,519,443 )

How can I increase my downloads?


My notes