Sh:1264

• Asgharzadeh, M., Golshani, M., & Shelah, S. Failure of singular compactness for Hom. Preprint. arXiv: 2506.03633
• Abstract:
  Assuming Gödel’s axiom of constructibility \bold V=\bold L, we construct an almost-free abelian group G of singular cardinality, such that for any nontrivial subgroup G' \subseteq G of smaller size, we have Hom(G',\mathbb{Z} )\ne 0, while Hom(G, \mathbb{Z}) = 0. This provides a consistent counterexample to the singular compactness of Hom.
• published version (14p)

@article{Sh:1264,
 author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon},
 title = {{Failure of singular compactness for Hom.}},
 note = {\href{https://arxiv.org/abs/2506.03633}{arXiv: 2506.03633}},
 arxiv_number = {2506.03633}
}