Journal of Symbolic Logic

Dominating and Unbounded Free Sets

Slawomir Solecki and Otmar Spinas

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We prove that every analytic set in $^\omega\omega \times ^\omega\omega$ with $\sigma$-bounded sections has a not $\sigma$-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 $\sigma$-bounded analytic free set. Under projective determinacy analytic can be replaced in the above results by projective.

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J. Symbolic Logic, Volume 64, Issue 1 (1999), 75-80.

First available in Project Euclid: 6 July 2007

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Solecki, Slawomir; Spinas, Otmar. Dominating and Unbounded Free Sets. J. Symbolic Logic 64 (1999), no. 1, 75--80.

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