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1 results

  • MADNESS IN VECTOR SPACES

  • IIAN B. SMYTHE
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 4 / December 2019
    Published online by Cambridge University Press:
    29 August 2019, pp. 1590-1611
    Print publication:
    December 2019

  • 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.