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).
Categories: math.LO math.AC math.CT math.RA math.RT