Journal of Symbolic Logic 68 (4):1065-1081 (2003)

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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 $\Sigma_n^1-set$ 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 theory   large cardinals   inner models
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DOI 10.2178/jsl/1067620173
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Projectively Well-Ordered Inner Models.J. R. Steel - 1995 - Annals of Pure and Applied Logic 74 (1):77-104.
The Consistency Strength of Projective Absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
The Core Model for Almost Linear Iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.

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