Mathematics – Logic
Scientific paper
2001-12-22
Mathematics
Logic
Scientific paper
Let T be an abelian group and lambda an uncountable regular cardinal. We consider the question of whether there is a lambda-universal group G^* among all torsion-free abelian groups G of cardinality less than or equal to lambda satisfying Ext(G,T)=0. Here G^* is said to be lambda-universal for T if, whenever a torsion-free abelian group G of cardinality less than or equal to lambda satisfies Ext(G,T)=0, then there is an embedding of G into G^*. For large classes of abelian groups T and cardinals lambda it is shown that the answer is consistently no. In particular, for T torsion, this solves a problem of Kulikov.
Shelah Saharon
Strüngmann Lutz
No associations
LandOfFree
Kulikov's problem on universal torsion-free abelian groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Kulikov's problem on universal torsion-free abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Kulikov's problem on universal torsion-free abelian groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-50198