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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a fragment of the universal Baire property for $ \Sigma^1_2$ sets


Author: Stuart Zoble
Journal: Proc. Amer. Math. Soc. 136 (2008), 1807-1814
MSC (2000): Primary 03E45; Secondary 03E35
Published electronically: January 17, 2008
MathSciNet review: 2373612
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Abstract: There is a well-known global equivalence between $ \Sigma^1_2$ sets having the universal Baire property, two-step $ \Sigma^1_3$ generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of $ \Sigma^1_2$ sets being $ (2^{\omega})^{+}$-cc-universally Baire, which is below $ 0^{\char93 }$. In a model obtained, there is a $ \Sigma^1_2$ set which is weakly $ \omega_2$-universally Baire but not $ \omega_2$-universally Baire.


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Additional Information

Stuart Zoble
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 2E4
Email: szoble@math.toronto.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-08918-1
PII: S 0002-9939(08)08918-1
Keywords: Generic absoluteness, universal Baire property
Received by editor(s): March 20, 2006
Received by editor(s) in revised form: September 12, 2006
Published electronically: January 17, 2008
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.