Failure of singular compactness for Hom
Abstract
Abstract Assuming Gödel's axiom of constructibility , we construct a ‐free abelian group of singular cardinality for some suitable cardinal which is regular and uncountable, equipped with the property that for every nontrivial subgroup of smaller cardinality, , while . This provides a consistent counterexample to the singular compactness of nontrivial duality with respect to the functor .
Fields of Study & Subjects
Advanced Topology and Set Theory
Rings
Modules
and Algebras
Advanced Banach Space Theory
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN