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MADNESS IN VECTOR SPACES
Published online by Cambridge University Press: 29 August 2019
Abstract
We consider maximal almost disjoint families of block 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 ω. We apply the author’s local Ramsey theory for vector spaces [32] to give partial results concerning their definability.
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