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Preprint Number 2256
2256. Michael C. Laskowski and Danielle S. Ulrich Borel complexity of modules E-mail: Submission date: 14 September 2022 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. Mathematics Subject Classification: 03E15 13C05 Keywords and phrases: |

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