Approximation properties of torsion classes

2024/06/05 by Sean Cox, Cox, Sean, Alejandro Poveda +3 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Logic (math.LO) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2406.02829

openalex publication_date 2024/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We strengthen a result of Bagaria and Magidor~\citeMR3152715 about the relationship between large cardinals and torsion classes of abelian groups, and prove that (1) the Maximum Deconstructibility principle introduced in \citeCox_MaxDecon requires large cardinals; it sits, implication-wise, between Vopěnka's Principle and the existence of an ω₁-strongly compact cardinal. (2) While deconstructibility of a class of modules always implies the precovering property by \citeMR2822215, the concepts are (consistently) non-equivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits.

Cited by

• Compactness in abelian group theory

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