Universally Baire sets and definable well-orderings of the reals

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 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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References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.
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.
A very absolute Pi-1-2 real singleton.René David - 1982 - Annals of Mathematical Logic 23 (2-3):101-120.

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