The $t$-structures generated by objects

Let $\mathscr {T}$ be a well generated triangulated category, and let $S\subset \mathscr set of objects. We prove that there is $t$-structure on with {T}^{\leq 0}=\overline {\langle S \rangle }^{(-\infty ,0]}$. This article an improvement the main result Alonso, Jeremías Souto [Trans. Amer. Soc. 355 (2003), pp. 2523–2543], in which theorem was proved under assumption has nice enough model. It should mentioned been influential—it turns out to interesting study all these $t$-structures.