# 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}:

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

{\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”.

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

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Bib entry

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