A minimal counterexample to universal baireness

Journal of Symbolic Logic 64 (4):1601-1627 (1999)
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Abstract

For a canonical model of set theory whose projective theory of the real numbers is stable under set forcing extensions, a set of reals of minimal complexity is constructed which fails to be universally Baire. The construction uses a general method for generating non-universally Baire sets via the Levy collapse of a cardinal, as well as core model techniques. Along the way it is shown (extending previous results of Steel) how sufficiently iterable fine structure models recognize themselves as global core models

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Citations of this work

Projective uniformization revisited.Kai Hauser & Ralf-Dieter Schindler - 2000 - Annals of Pure and Applied Logic 103 (1-3):109-153.
Homogeneously Suslin sets in tame mice.Farmer Schlutzenberg - 2012 - Journal of Symbolic Logic 77 (4):1122-1146.

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References found in this work

The problem of predicativity.Joseph R. Shoenfield - 1961 - In Bar-Hillel, Yehoshua & [From Old Catalog] (eds.), Essays on the Foundations of Mathematics. Jerusalem,: Magnes Press. pp. 132--139.
Inner models with many Woodin cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
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.
Strong cardinals in the core model.Kai Hauser & Greg Hjorth - 1997 - Annals of Pure and Applied Logic 83 (2):165-198.

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