TY - JOUR
T1 - Expressive power of infinitary logic and absolute co-Hopfianity
AU - Asgharzadeh, Mohsen
AU - Golshani, Mohammad
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2025 by the University of Illinois Urbana-Champaign.
PY - 2025/6/1
Y1 - 2025/6/1
N2 - Recently, Paolini and Shelah constructed absolutely Hopfian torsion-free abelian groups of any given size. In contrast, we show that this is not necessarily the case for absolutely co-Hopfian groups. We use the infinitary logic to show that there are no absolute co-Hopfian abelian groups above the first beautiful cardinal. An extension of this result to the category of modules over a commutative ring is given.
AB - Recently, Paolini and Shelah constructed absolutely Hopfian torsion-free abelian groups of any given size. In contrast, we show that this is not necessarily the case for absolutely co-Hopfian groups. We use the infinitary logic to show that there are no absolute co-Hopfian abelian groups above the first beautiful cardinal. An extension of this result to the category of modules over a commutative ring is given.
UR - http://www.scopus.com/inward/record.url?scp=105008706897&partnerID=8YFLogxK
U2 - 10.1215/00192082-11918990
DO - 10.1215/00192082-11918990
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AN - SCOPUS:105008706897
SN - 0019-2082
VL - 69
SP - 269
EP - 302
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
IS - 2
ER -