  We give a reduction technique for silting intervals in extriangulated
categories, which we call "silting interval reduction". It provides a reduction
technique for tilting subcategories when the extriangulated categories are
exact categories.
  In 0-Auslander extriangulated categories (a generalization of the well-known
two-term category $K^{[-1,0]}(\mathsf{proj}\Lambda)$ for an Artin algebra
$\Lambda$), we provide a reduction theory for silting objects as an application
of silting interval reduction. It unifies two-term silting reduction and
Iyama-Yoshino's 2-Calabi-Yau reduction. The mutation theory developed by
Gorsky, Nakaoka and Palu recently can be deduced from it. Since there are
bijections between the silting objects and the support $\tau$-tilting modules
over certain finite dimensional algebras, we show it is compatible with
$\tau$-tilting reduction. This compatibility theorem also unifies the two
compatibility theorems obtained by Jasso in his work on $\tau$-tilting
reduction.
  We give a new construction for 0-Auslander extriangulated categories using
silting mutation, together with silting interval reduction, we obtain some
results on silting quivers. Finally, we prove that $d$-Auslander extriangulated
categories are related to a certain sequence of silting mutations.
