  We study certain Banach spaces that are added in the extension by one Cohen
real. Specifically, we show that adding just one Cohen real to any model adds a
Banach space of density $\aleph_1$ which does not embed into any such space in
the ground model such a Banach space can be chosen to be UG This has
consequences on the the isomorphic universality number for Banach spaces of
density $\aleph_1$, which is hence equal to $\aleph_2$ in the standard Cohen
model and the same is true for UG spaces. Analogous universality results for
Banach spaces are true for other cardinals, by a different proof.
