Analytic countably splitting families

@article{Spinas2004AnalyticCS,
  title={Analytic countably splitting families},
  author={Otmar Spinas},
  journal={Journal of Symbolic Logic},
  year={2004},
  volume={69},
  pages={101 - 117}
}
  • O. Spinas
  • Published 1 March 2004
  • Mathematics
  • Journal of Symbolic Logic
Abstract A family A ⊆ (ω) is called countably splitting if for every countable F ⊆ [ω]ω, some element of A splits every member of F. We define a notion of a splitting tree, by means of which we prove that every analytic countably splitting family contains a closed countably splitting family. An application of this notion solves a problem of Blass. On the other hand we show that there exists an Fσ splitting family that does not contain a closed splitting family. 
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