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Saturation, Suslin trees and meager sets

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Abstract.

We show, using a variation of Woodin’s partial order ℙ max , that it is possible to destroy the saturation of the nonstationary ideal on ω1 by forcing with a Suslin tree. On the other hand, Suslin trees typcially preserve saturation in extensions by ℙ max variations where one does not try to arrange it otherwise. In the last section, we show that it is possible to have a nonmeager set of reals of size ℵ1, saturation of the nonstationary ideal, and no weakly Lusin sequences, answering a question of Shelah and Zapletal.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Miami University, Oxford, OH, 45056, USA

    Paul Larson

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  1. Paul Larson
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Correspondence to Paul Larson.

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Supported by the Japan Society for the Promotion of Science, the Mittag-Leffler Institute and the São Paulo State Research Support Foundation (FAPESP, Grant # 02/11551-3).

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Larson, P. Saturation, Suslin trees and meager sets. Arch. Math. Logic 44, 581–595 (2005). https://doi.org/10.1007/s00153-004-0257-8

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  • DOI: https://doi.org/10.1007/s00153-004-0257-8

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