The Nonstationary Ideal in the Pmax Extension

Journal of Symbolic Logic 72 (1):138 - 158 (2007)
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Abstract

The forcing construction Pmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω₁ is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω₁ in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension

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10.2178/jsl/1174668389

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Citations of this work

Martin’s Maximum and definability in H.Paul B. Larson - 2008 - Annals of Pure and Applied Logic 156 (1):110-122.

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References found in this work

The canonical function game.Paul B. Larson - 2005 - Archive for Mathematical Logic 44 (7):817-827.
Woodin cardinals and presaturated ideals.Noa Goldring - 1992 - Annals of Pure and Applied Logic 55 (3):285-303.
A basis theorem for perfect sets.Marcia J. Groszek & Theodore A. Slaman - 1998 - Bulletin of Symbolic Logic 4 (2):204-209.

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