## Journal of Symbolic Logic

### Universally Baire sets and definable well-orderings of the reals

#### 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.

#### Article information

Source
J. Symbolic Logic, Volume 68, Issue 4 (2003), 1065-1081.

Dates
First available in Project Euclid: 31 October 2003

https://projecteuclid.org/euclid.jsl/1067620173

Digital Object Identifier
doi:10.2178/jsl/1067620173

Mathematical Reviews number (MathSciNet)
MR2017341

Zentralblatt MATH identifier
1055.03028

#### Citation

Friedman, Sy D.; Schindler, Ralf. Universally Baire sets and definable well-orderings of the reals. J. Symbolic Logic 68 (2003), no. 4, 1065--1081. doi:10.2178/jsl/1067620173. https://projecteuclid.org/euclid.jsl/1067620173

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