A minimal counterexample to universal baireness

Journal of Symbolic Logic 64 (4):1601-1627 (1999)
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
Keywords Set Theory   Descriptive Set Theory   Inner Models   Universally Baire Sets
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