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 how sufficiently iterable fine structure models recognize themselves as global core models.

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