Dominating and Unbounded Free Sets

Solecki, Slawomir; Spinas, Otmar

J. Symbolic Logic, Tome 64 (1999) no. 1, p. 75-80 / Harvested from Project Euclid

Résumé

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.

Publié le : 1999-03-14
Classification:

@article{1183745693,
     author = {Solecki, Slawomir and Spinas, Otmar},
     title = {Dominating and Unbounded Free Sets},
     journal = {J. Symbolic Logic},
     volume = {64},
     number = {1},
     year = {1999},
     pages = { 75-80},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745693}
}

Solecki, Slawomir; Spinas, Otmar. Dominating and Unbounded Free Sets. J. Symbolic Logic, Tome 64 (1999) no. 1, pp.  75-80. http://gdmltest.u-ga.fr/item/1183745693/