Woodin cardinals and presaturated ideals

Annals of Pure and Applied Logic 55 (3):285-303 (1992)
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Abstract

Models of set theory are constructed where the non-stationary ideal on PΩ1λ is presaturated. The initial model has a Woodin cardinal. Using the Lévy collapse the Woodin cardinal becomes λ+ in the final model. These models provide new information about the consistency strength of a presaturated ideal onPΩ1λ for λ greater than Ω1

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10.1016/0168-0072(92)90039-3

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The Nonstationary Ideal in the Pmax Extension.Paul B. Larson - 2007 - Journal of Symbolic Logic 72 (1):138 - 158.

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References found in this work

Precipitous ideals.T. Jech, M. Magidor, W. Mitchell & K. Prikry - 1980 - Journal of Symbolic Logic 45 (1):1-8.
Countable approximations and Löwenheim-Skolem theorems.David W. Kueker - 1977 - Annals of Mathematical Logic 11 (1):57.

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