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Salce's problem on cotorsion pairs is undecidable (2103.06687v3)
Published 11 Mar 2021 in math.LO, math.AC, math.CT, math.RA, and math.RT
Abstract: 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).
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