Borel complexity of modules
Logic
2022-09-16 v1 Commutative Algebra
Abstract
We prove that for a countable, commutative ring , the class of countable -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 , both the class of left -modules endowed with an endomorphism and the class of left -modules with four named submodules are Borel complete.
Cite
@article{arxiv.2209.06898,
title = {Borel complexity of modules},
author = {Michael C. Laskowski and Danielle S. Ulrich},
journal= {arXiv preprint arXiv:2209.06898},
year = {2022}
}