This is an announcement for the paper “A 1-separably injective space that does not contain $\ell_\infty$” by Antonio Aviléshttps://arxiv.org/find/math/1/au:+Aviles_A/0/1/0/all/0/1, Piotr Koszmiderhttps://arxiv.org/find/math/1/au:+Koszmider_P/0/1/0/all/0/1.

Abstract: We study the $\omega_2$-subsets of tightly $\sigma$-filtered Boolean algebras and, as an application, we show the consistency of the existence of a Banach space that is $1$-separably injective but does not contain any isomorphic copy of $\ell_\infty$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1609.02685