Failure of singular compactness for Hom

Mohsen Asgharzadeh; Mohammad Golshani; Saharon Shelah

doi:10.1112/blms.70324

Failure of singular compactness for Hom

Mohsen Asgharzadeh
, Mohammad Golshani^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Assuming Gödel's axiom of constructibility (Formula presented.), we construct a (Formula presented.) -free abelian group (Formula presented.) of singular cardinality for some suitable cardinal (Formula presented.) which is regular and uncountable, equipped with the property that for every nontrivial subgroup (Formula presented.) of smaller cardinality, (Formula presented.), while (Formula presented.). This provides a consistent counterexample to the singular compactness of nontrivial duality with respect to the functor (Formula presented.).

Original language	English
Article number	e70324
Journal	Bulletin of the London Mathematical Society
Volume	58
Issue number	3
DOIs	https://doi.org/10.1112/blms.70324
State	Published - Mar 2026

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© 2026 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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10.1112/blms.70324

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Failure of singular compactness for Hom

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