Sh:936

• Enayat, A., & Shelah, S. (2011). An improper arithmetically closed Borel subalgebra of \mathcal P(\omega)\bmod\mathrm{FIN}. Topology Appl., 158(18), 2495–2502. DOI: 10.1016/j.topol.2011.08.006 MR: 2847322
• Abstract:
  We show the existence of a subalgebra {\mathcal A}\subset {\mathcal P}(\omega) that satisfies the following three conditions.

  {\mathcal A} is Borel (when {\mathcal P}(\omega) is identified with 2^\omega).

  {\mathcal A} is arithmetically closed (i.e., {\mathcal A} is closed under the Turing jump, and Turing reducibility).

  The forcing notion ({\mathcal A}, \subset) modulo the ideal FIN of finite sets collapses the continuum to \aleph_0.

• published version (8p)

@article{Sh:936,
 author = {Enayat, Ali and Shelah, Saharon},
 title = {{An improper arithmetically closed Borel subalgebra of $\mathcal P(\omega)\bmod\mathrm{FIN}$}},
 journal = {Topology Appl.},
 fjournal = {Topology and its Applications},
 volume = {158},
 number = {18},
 year = {2011},
 pages = {2495--2502},
 issn = {0166-8641},
 mrnumber = {2847322},
 mrclass = {03E15 (03C55 28A05 54H05)},
 doi = {10.1016/j.topol.2011.08.006}
}