  Salce \cite{MR565595} introduced the notion of a \emph{cotorsion pair} of
classes of abelian groups, and asked whether every such pair is \emph{complete}
(i.e., has enough injectives and projectives). We prove that it is consistent,
relative to the consistency of Vop\v{e}nka's Principle (VP), that the answer is
affirmative. Combined with a previous result of Eklof-Shelah \cite{MR2031314},
this shows that Salce's Problem is independent of the ZFC axioms (modulo the
consistency of VP).
