  Let $\mathcal T$ be a well generated triangulated category, and let
$S\subset\mathcal T$ be a set of objects. We prove that there is a t-structure
on $\mathcal T$ with ${\mathcal T}^{\leq0}=\overline{\langle
S\rangle}^{(-\infty,0]}$.
  This article is an improvement on the main result of a 2003 article by
Alonso, Jeremias and Souto---in that article the theorem was proved under the
assumption that $\mathcal T$ has a nice enough model. It should be mentioned
that the theorem of Alonso, Jeremias and Souto has been influential---it turns
out to be interesting to study all of these t-structures.
