论文标题
模块的Borel复杂性
Borel complexity of modules
论文作者
论文摘要
我们证明，对于可数值的，可交换的环$ r $，可数$ r $ $模型的类要么只有许多同构类型，否则它已经完成了。该机械简洁地证明了TFAB的Borel完整性，TFAB是无扭转的Abelian群体。我们还证明，对于任何可数的环$ r $，两个左$ r $ - 模块都赋予了内态性，而左$ r $ - 模块的类别均带有四个命名子模型。
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.
