Sh:1010

• Shelah, S., & Usuba, T. \omega_1-Stationary preserving \sigma-Baire posets of size \aleph_1. Preprint.
• Abstract:
  

  We prove that the following theories are equiconsistent with {\rm ZFC}:

  1. {\rm ZFC}+{\rm CH}+ “there is an \omega _1-stationary preserving \sigma-Baire poset of size \aleph_1 which is not semiproper”.

  2. {\rm ZFC}+“Martin’s axiom for semiproper posets of size \aleph_1” + “there is an \omega _1-stationary preserving \sigma-Baire poset of size \aleph_1 which is not semiproper”.

  3. {\rm ZFC}+{\rm CH}+“every \omega _1-stationary preserving \sigma-Baire poset of size \aleph_1 is semiproper”.

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@article{Sh:1010,
 author = {Shelah, Saharon and Usuba, Toshimichi},
 title = {{$\omega_1$-Stationary preserving $\sigma$-Baire posets of size $\aleph_1$ }}
}