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Universally Baire sets and definable well-orderings of the reals

Published online by Cambridge University Press:  12 March 2014

SY D. Friedman  and
Ralf Schindler
SY D. Friedman
Affiliation:
Institut Für Formale Logik, Universität Wien, Währinger STR. 25, 1090 Wien, Austria, E-mail: sdf@logic.univie.ac.at
Ralf Schindler
Affiliation:
Institut Für Formale Logik, Universität Wien, Währinger STR. 25, 1090 Wien, Austria, E-mail: rds@logic.univie.ac.at
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Abstract

Let n ≥ 3 be an integer. We show that it is consistent (relative to the consistency of n − 2 strong cardinals) that every Σ1n-set of reals is universally Baire yet there is a (lightface) projective well-ordering of the reals. The proof uses “David's trick” in the presence of inner models with strong cardinals.

Keywords

Descriptive set theorylarge cardinalsinner models
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 4 , December 2003 , pp. 1065 - 1081
Copyright
Copyright © Association for Symbolic Logic 2003

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