On the cogeneration of cotorsion pairs [article]

Paul C. Eklof and Saharon Shelah and Jan Trlifaj
2004 arXiv   pre-print
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.
arXiv:math/0405117v1 fatcat:b3pl4qgyhbh7bdfx2fscdaxu4a