  Truncation in Generalized Series fields is a robust notion, in the sense that
it is preserved under various algebraic and some transcendental extensions. In
this paper, we study conditions that ensure that a truncation closed set
extends naturally to a truncation closed differential ring, and a truncation
closed differential field has a truncation closed Liouville closure. In
particular, we introduce the Notion of IL-closedness in Unions of Hahn fields
in order to determine that this condition is sufficient to preserve truncation
in those two settings for constructions such as the field of
logarithmic-exponential transseries.
