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Ideals without ccc and without property $ \boldsymbol( \mathbf{M} \boldsymbol)$


Author: Howard Becker
Journal: Proc. Amer. Math. Soc. 128 (2000), 3031-3034
MSC (2000): Primary 03E15
Published electronically: April 28, 2000
MathSciNet review: 1670422
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Abstract: We prove a strong version of a theorem of Balcerzak-Roslanowski-Shelah by showing, in ZFC, that there exists a simply definable Borel $\sigma $-ideal for which both the ccc and property (M) fail. The proof involves Polish group actions.


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Additional Information

Howard Becker
Affiliation: Department of Mathematics, The University of South Carolina, Columbia, South Carolina 29208
Email: becker@math.sc.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05373-9
Keywords: Ideal of sets, Polish group action
Received by editor(s): October 23, 1998
Received by editor(s) in revised form: December 3, 1998
Published electronically: April 28, 2000
Additional Notes: The author’s research was partially supported by NSF Grant DMS-9505505.
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society