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The nonstationary ideal in the ℙmax extension

Published online by Cambridge University Press:  12 March 2014

Paul B. Larson
Paul B. Larson*
Affiliation:
Miami University, Department of Mathematics and Statistics, Oxford, Ohio 45056, USA. E-mail: larsonpb@muohio.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 138 - 158
Copyright
Copyright © Association for Symbolic Logic 2007

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