This is an announcement for the paper “Tsirelson-like spaces and complexity of classes of Banach spaces” by Ondřej Kurkahttps://arxiv.org/find/math/1/au:+Kurka_O/0/1/0/all/0/1.

Abstract: Employing a construction of Tsirelson-like spaces due to Argyros and Deliyanni, we show that the class of all Banach spaces which are isomorphic to a subspace of $c_0$ is a complete analytic set with respect to the Effros Borel structure of separable Banach spaces. Moreover, the classes of all separable spaces with the Schur property and of all separable spaces with the Dunford-Pettis property are $\Pi_2^1$-complete.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1612.09334