Saturation, Suslin trees and meager sets

Archive for Mathematical Logic 44 (5):581-595 (2005)

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 ω 1 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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References found in this work

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
Precipitous Ideals.T. Jech, M. Magidor, W. Mitchell & K. Prikry - 1980 - Journal of Symbolic Logic 45 (1):1-8.
An Variation for One Souslin Tree.Paul Larson - 1999 - Journal of Symbolic Logic 64 (1):81-98.
Canonical Models for ℵ1-Combinatorics.Saharon Shelah & Jindr̆ich Zapletal - 1999 - Annals of Pure and Applied Logic 98 (1-3):217-259.

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Citations of this work

Ns Saturated and -Definable.Stefan Hoffelner - 2021 - Journal of Symbolic Logic 86 (1):25-59.
ℙmax Variations Related to Slaloms.Teruyuki Yorioka - 2006 - Mathematical Logic Quarterly 52 (2):203-216.

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