On a fragment of the universal Baire property for 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 | References | Similar Articles | Additional Information

Abstract: There is a well-known global equivalence between sets having the universal Baire property, two-step generic absoluteness, and the closure of the universe under the sharp operation. In this note, we determine the exact consistency strength of sets being -cc-universally Baire, which is below . In a model obtained, there is a set which is weakly -universally Baire but not -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:
https://doi.org/10.1090/S0002-9939-08-08918-1

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.