# 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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