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6. Precipitouness of NS


    1. Add remark

      Problem 6.4.

      [Larson] Assume \text{NS}_{\omega_1} is precipitous. Is it possible to force \text{NS}_{\omega_1} to be non-precipitous without adding subsets of \omega_1?
        1. Remark. [Larson] It is consistent for this to be impossible, e.g. if NS_{\omega_1}^+ has a dense subset of size \aleph_1. Also, any such forcing must always add a subset of size \omega_1?

              Cite this as: AimPL: From ℵ2 to infinity, available at http://aimpl.org/alephtwo.