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>>