# 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)

Bib entry

@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}, doi = {10.1016/j.topol.2011.08.006}, mrclass = {03E15 (03C55 28A05 54H05)}, mrnumber = {2847322}, doi = {10.1016/j.topol.2011.08.006} }