A minimal counterexample to universal baireness

Journal of Symbolic Logic 64 (4):1601-1627 (1999)
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
Keywords Set Theory   Descriptive Set Theory   Inner Models   Universally Baire Sets
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DOI 10.2307/2586801
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References found in this work BETA
J. R. Steel (1993). Inner Models with Many Woodin Cardinals. Annals of Pure and Applied Logic 65 (2):185-209.
J. R. Steel (1995). Projectively Well-Ordered Inner Models. Annals of Pure and Applied Logic 74 (1):77-104.
Kai Hauser (1995). The Consistency Strength of Projective Absoluteness. Annals of Pure and Applied Logic 74 (3):245-295.
Kai Hauser & Greg Hjorth (1997). Strong Cardinals in the Core Model. Annals of Pure and Applied Logic 83 (2):165-198.

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