Salce's problem on cotorsion pairs is undecidable. Issue 4 (18th April 2022) - Cox, Sean
Abstract: In the 1970's, Salce introduced the notion of a cotorsion pair of classes of abelian groups, and asked whether every such pair is complete (that is, has enough injectives and projectives); we refer to this as Salce's Problem (for Ab ). We prove that it is consistent, relative to the consistency of Vopěnka's Principle (VP), that the answer is affirmative. Combined with a previous result of Eklof and Shelah , this shows that Salce's Problem for Ab, and in fact for R‐Mod when R R is hereditary, is independent of the ZFC axioms (modulo the consistency of VP).