On the cogeneration of cotorsion pairs (Q1882879)

It is known that if a cotorsion pair over a Dedekind domain is generated by a class of cotorsion (i.e.\ homomorphic image of pure-injective) modules then it is cogenerated by a set. The authors show in theorem 1.3 that this cannot be reasonably strengthened: It is consistent with ZFC (the usual axioms of set theory) that over any Dedekind domain with just countably many prime ideals, for all cotorsion pair generated and cogenerated by a set of modules, all cogenerators must be cotorsion. The proof requires a good understanding of cotorsion modules and only basic knowledge of set theory (stationary sets, clubs). The article is concise and well-written.