Dominating and unbounded free sets

@article{Solecki1999DominatingAU,
  title={Dominating and unbounded free sets},
  author={Slawomir Solecki and Otmar Spinas},
  journal={Journal of Symbolic Logic},
  year={1999},
  volume={64},
  pages={75 - 80}
}
Abstract We prove that every analytic set in ωω × ωω with σ-bounded sections has a not σ-bounded closed free set. We show that this result is sharp. There exists a closed set with bounded sections which has no dominating analytic free set. and there exists a closed set with non-dominating sections which does not have a not σ-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective. 
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