Work

Approximation properties of torsion classes

Year: 2024

Type: article

Abstract: We strengthen a result of Bagaria and Magidor (Trans. Amer. Math. Soc. 366 (2014), no. 4, 1857–1877) about the relationship between large cardinals and torsion classes of abelian groups, and prove that the Maximum Deconstructibility principle introduced in Cox (J. Pure Appl. Algebra 226 (2022), no. 5) requires large cardinals; it sits, implication‐wise, between Vopěnka's Principle and the existence of an ‐strongly compact cardinal. While deconstructibility of a class of modules always implies the precovering property by Saorín and Šťovíček (Adv. Math. 228 (2011), no. 2, 968–1007), the concepts are (consistently) nonequivalent, even for classes of abelian groups closed under extensions, homomorphic images, and colimits.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.13169

Authors: Sean Cox, Alejandro Poveda, Jan Trlifaj

Institutions: Virginia Commonwealth University, Harvard University, Charles University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,780

Funders: National Science Foundation, Grantová Agentura České Republiky