Paul C. Eklof

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It is proved consistent with ZFC + GCH that for every Whitehead group A of infinite rank, there is a Whitehead group H A such that Ext(H A , A) = 0. This is a strong generalization of the consistency of the existence of non-free Whitehead groups. A consequence is that it is undecidable in ZFC + GCH whether every Z-module has a ⊥ {Z}-precover. Moreover, for(More)
We consider the question of when the dual of a Whitehead group is a test group for Whitehead groups. This turns out to be equivalent to the question of when the tensor product of two Whitehead groups is Whitehead. We investigate what happens in different models of set theory.
Let R be a Dedekind domain. In [6], 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(More)