  Let K be differential field with algebraically closed field of constants. Let
K^diff be a differential closure of K, and L the (iterated) Picard-Vessiot
closure of K inside K^diff. Let G be a linear differential algebraic group over
K and X a differential algebraic torsor for G over K. We prove that X(L) is
Kolchin-dense in X. When G is finite-dimensional we prove that X(L) =
X(K^diff). We give close relationships between Picard-Vessiot extensions of K
and torsors for suitable finite-dimensional linear differential algebraic
groups over K. We suggest some differential field analogues of the notion of
boundedness for fields (Serre's property F).
