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Dominating and unbounded free sets

Published online by Cambridge University Press:  12 March 2014

Slawomir Solecki  and
Otmar Spinas
Slawomir Solecki
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA E-mail: ssolecki@indiana.edu Mathematik, ETH Zentrum, 8092 Zürich, Switzerland E-mail: spinas@math.ethz.ch
Otmar Spinas
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA Department of Mathematics, University of California, Irvine, CA 92717., USA
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 75 - 80
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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