TY - JOUR
T1 - On the existence of precovers
AU - Eklof, Paul C.
AU - Shelah, Saharon
PY - 2003
Y1 - 2003
N2 - It is proved consistent with ZFC + GCH that for every Whitehead group A of infinite rank, there is a Whitehead group HA 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 a large class of ℤ-modules N, it is proved consistent that a known sufficient condition for the existence of ⊥{N}-precovers is not satisfied.
AB - It is proved consistent with ZFC + GCH that for every Whitehead group A of infinite rank, there is a Whitehead group HA 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 a large class of ℤ-modules N, it is proved consistent that a known sufficient condition for the existence of ⊥{N}-precovers is not satisfied.
UR - http://www.scopus.com/inward/record.url?scp=0345782296&partnerID=8YFLogxK
U2 - 10.1215/ijm/1258488146
DO - 10.1215/ijm/1258488146
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AN - SCOPUS:0345782296
SN - 0019-2082
VL - 47
SP - 173
EP - 188
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 1-2
ER -