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A minimal counterexample to universal baireness

Published online by Cambridge University Press:  12 March 2014

Kai Hauser
Kai Hauser*
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA, E-mail: hauser@math.berkeley.edu Lehrstuhl Für Mathematische Logik, Humboldt Universität, 10099 Berlin, Germany, E-mail: Hauser@Mathematik.Hu-berlin.de
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Abstract

For a canonical model of set theory whose projective theory of the real numbers is stable under set forcing extensions, a set of reals of minimal complexity is constructed which fails to be universally Baire. The construction uses a general method for generating non-universally Baire sets via the Levy collapse of a cardinal, as well as core model techniques. Along the way it is shown (extending previous results of Steel) how sufficiently iterable fine structure models recognize themselves as global core models.

Keywords

Set theorydescriptive set theoryinner modelsuniversally Baire sets
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1601 - 1627
Copyright
Copyright © Association for Symbolic Logic 1999

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