Borel complexity of modules

Annals of Pure and Applied Logic 2026 Open access

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Authors: Michael Chris Laskowski, Danielle Ulrich
DOI: 10.1016/j.apal.2026.103780
Cited by: 0
References: 8

Abstract

We prove that for a countable, commutative ring $R$, the class of countable $R$-modules either has only countably many isomorphism types, or else it is Borel complete. The machinery gives a succinct proof of the Borel completeness of TFAB, the class of torsion-free abelian groups. We also prove that for any countable ring $R$, both the class of left $R$-modules endowed with an endomorphism and the class of left $R$-modules with four named submodules are Borel complete.

Fields of Study & Subjects

Computability Logic AI Algorithms Rings Modules and Algebras Advanced Topology and Set Theory

Publication details

Journal / source
Annals of Pure and Applied Logic
Publisher
Elsevier BV
Volume
177
Issue
9
Pages
103780–103780
Publication date
29 April 2026
Language
EN