Sh:1264

• Asgharzadeh, M., Golshani, M., & Shelah, S. (2026). Failure of singular compactness for Hom. Bull. Lond. Math. Soc., 58(3), e70324. arXiv: 2506.03633 DOI: 10.1112/blms.70324
• 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 (16p)

@article{Sh:1264,
 author = {Asgharzadeh, Mohsen and Golshani, Mohammad and Shelah, Saharon},
 title = {{Failure of singular compactness for Hom.}},
 journal = {Bull. Lond. Math. Soc.},
 fjournal = {Bulletin of the London Mathematical Society},
 volume = {58},
 number = {3},
 year = {2026},
 pages = {e70324},
 mrclass = {03E75, 20A15, 20K20, 20K40},
 doi = {10.1112/blms.70324},
 note = {\href{https://arxiv.org/abs/2506.03633}{arXiv: 2506.03633}},
 arxiv_number = {2506.03633}
}