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