## Journal of Symbolic Logic

### Dominating and Unbounded Free Sets

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745693

Mathematical Reviews number (MathSciNet)
MR1683896

Zentralblatt MATH identifier
0947.03067

JSTOR