Universally Baire sets and definable well-orderings of the reals

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

Abstract
Let n ≥ 3 be an integer. We show that it is consistent that every σ1n-set of reals is universally Baire yet there is a projective well-ordering of the reals. The proof uses “David’s trick” in the presence of inner models with strong cardinals.
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DOI 10.2178/jsl/1067620173
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References found in this work BETA

Projectively Well-Ordered Inner Models.J. R. Steel - 1995 - Annals of Pure and Applied Logic 74 (1):77-104.
The Core Model for Almost Linear Iterations.Ralf-Dieter Schindler - 2002 - Annals of Pure and Applied Logic 116 (1-3):205-272.
The Consistency Strength of Projective Absoluteness.Kai Hauser - 1995 - Annals of Pure and Applied Logic 74 (3):245-295.
Projective Uniformization Revisited.Kai Hauser & Ralf-Dieter Schindler - 2000 - Annals of Pure and Applied Logic 103 (1-3):109-153.
A Very Absolute Pi-1-2 Real Singleton.René David - 1982 - Annals of Mathematical Logic 23 (2-3):101-120.

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