Abstract
Let R be a Dedekind domain. Recently, Enochs' solution of the Flat Cover Conjecture was extended as follows: (∗) If C is a cotorsion pair generated by a class of cotorsion modules, then C is cogenerated by a set. We show that (∗) is the best result provable in ZFC in case R has a countable spectrum: the Uniformization Principle UP + implies that C is not cogenerated by a set whenever C is a cotorsion pair generated by a set which contains a non-cotorsion module.
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