A model with a precipitous ideal, but no normal precipitous ideal

Journal of Mathematical Logic 13 (1):1250008 (2013)
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Abstract

Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on ℵ1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q-point precipitous filters on ℵ1, i. e. those isomorphic to extensions of Cubℵ1.

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10.1142/s0219061312500080

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The negation of the singular cardinal hypothesis from o(K)=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
Precipitous ideals.T. Jech, M. Magidor, W. Mitchell & K. Prikry - 1980 - Journal of Symbolic Logic 45 (1):1-8.
On generic elementary embeddings.Moti Gitik - 1989 - Journal of Symbolic Logic 54 (3):700-707.
Collapsing functions.Ernest Schimmerling & Boban Velickovic - 2004 - Mathematical Logic Quarterly 50 (1):3-8.

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