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| Main Authors: | , , |
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| Format: | Preprint |
| Udgivet: |
2025
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| Fag: | |
| Online adgang: | https://arxiv.org/abs/2506.03633 |
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Indholdsfortegnelse:
- Assuming Gödel's axiom of constructibility $V=L$, we construct a $χ$-free abelian group $G$ of singular cardinality for some suitable cardinal $χ$ which is regular and uncountable, equipped with the property that for every nontrivial subgroup $G' \subseteq G$ of smaller cardinality, $Hom(G',\mathbb{Z}) \neq 0$, while $Hom(G,\mathbb{Z}) = 0$. This provides a consistent counterexample to the singular compactness of nontrivial duality with respect to the functor $Hom(-,\mathbb{Z})$.