On the undefinability of Tsirelson's space and its descendants

Peter Casazza, Jose Iovino

Published 2018-12-06Version 1

We prove that Tsirelson's space cannot be defined explicitly from the classical Banach sequence spaces. We also prove that any Banach space that is explicitly definable from a class of spaces that contain $\ell_p$ or $c_0$ must contain $\ell_p$ or $c_0$ as well.