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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Invariant ideals and Borel sets

Author: Andrzej Pelc
Journal: Proc. Amer. Math. Soc. 97 (1986), 503-506
MSC: Primary 04A15; Secondary 03E05, 28A05
MathSciNet review: 840637
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Abstract: We investigate the size of the algebra $ \mathcal{B}(I)$, where $ \mathcal{B}$ is the family of Borel sets and $ I$ is a translation invariant ideal of sets of reals. In particular the question whether $ \mathcal{B}(I)$ can contain Vitali selectors or even all sets of reals is discussed in connection with the completeness of $ I$ and its invariance.

References [Enhancements On Off] (What's this?)

  • 1. J. Brzuchowski and J. Cichoń, Miara $ i$ kategoria, unpublished.
  • [1] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. of Math. Logic 2 (1970), 143-178. MR 0270904 (42:5787)
  • [2] A. Pele, Invariant measures and ideals on discrete groups, Dissertationes Math. (in print).
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  • [4] A. Taylor, On the cardinality of the algebra $ \mathcal{P}(k)/I$, handwritten notes.

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Article copyright: © Copyright 1986 American Mathematical Society

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