Journal of Symbolic Logic

A Minimal Counterexample to Universal Baireness

Kai Hauser

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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.

Article information

J. Symbolic Logic, Volume 64, Issue 4 (1999), 1601-1627.

First available in Project Euclid: 6 July 2007

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Zentralblatt MATH identifier


Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 03E45: Inner models, including constructibility, ordinal definability, and core models 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05] 28A05: Classes of sets (Borel fields, $\sigma$-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05] 03E55: Large cardinals 03E60: Determinacy principles

Set Theory Descriptive Set Theory Inner Models Universally Baire Sets


Hauser, Kai. A Minimal Counterexample to Universal Baireness. J. Symbolic Logic 64 (1999), no. 4, 1601--1627.

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