### On the cogeneration of cotorsion pairs

by Eklof and Shelah and Trlifaj. [EShT:814]

J Algebra, 2004

Let R be a Dedekind domain. 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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