\(P\)-points in \(\mathbb Q_{\max}\) models
type: Item
instance of: scholarly article
title: \(P\)-points in \(\mathbb Q_{\max}\) models
zbMATH Open document ID: 1024.03048
DOI: 10.1016/S0168-0072(02)00036-2
published in: Annals of Pure and Applied Logic
publication date: 2003-03-09T00:00:00Z
review text: Shelah has proven that \(\omega_1\)-density of the nonstationary ideal on \(\omega_1\) implies the failure of the Continuum Hypothesis. The authors show that this density condition on the nonstationary ideal cannot decide the existence of \(P\)-points. The authors assume \(\text{AD}^{L(\mathbb R)}\) and use a method of Woodin for obtaining models from this hypothesis where the nonstationary ideal on \(\omega_1\) is \(\omega_1\)-dense to construct two canonical models, one with no \(P\)-point and one with a unique \(P\)-point.
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E55
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E60
zbMATH DE Number: 1878504
zbMATH Keywords: P-points
zbMATH Keywords: forcing
zbMATH Keywords: consistency
zbMATH Keywords: dense ideal
zbMATH Keywords: nonstationary ideal
author: Qi Feng
author: W. Hugh Woodin
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
cites work: Combinatorics on ideals and forcing
cites work: Q3852172
cites work: Q4375363
cites work: Canonical models for \(\aleph_1\)-combinatorics
cites work: The axiom of determinacy, forcing axioms, and the nonstationary ideal
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description: scientific article; zbMATH DE number 1878504