## Madness in vector spaces. (arXiv:1712.00057v1 [math.LO])

We consider maximal almost disjoint families of vector subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the "spectrum" of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on $\omega$. We apply the author's local Ramsey theory for vector spaces to give partial results concerning their definability.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 We consider maximal almost disjoint families of vector subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the "spectrum" of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on $\omega$. We apply the author's local Ramsey theory for vector spaces to give partial results concerning their definability.