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

Abstract
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
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DOI 10.1016/j.apal.2007.08.002
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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.

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