Nicely generated and chaotic ideals
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- by Jörg Brendle PDF
- Proc. Amer. Math. Soc. 124 (1996), 2533-2538 Request permission
Abstract:
We show that if the real line is the disjoint union of $\kappa$ meager sets such that every meager set is contained in a countable union of them, then $\kappa = \omega _1$. This answers a question addressed by Jacek Cichoń. We also prove two theorems saying roughly that any attempt to produce the isomorphism type of the meager ideal in the Cohen real and the random real extensions must fail. All our results hold for meager replaced by null, as well.References
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Additional Information
- Jörg Brendle
- Affiliation: Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
- Address at time of publication: Department of Mathematics, Bradley Hall, Dartmouth College, Hanover, New Hampshire 03755
- Email: jobr@michelangelo.mathematik.uni-tuebingen.de, brendle@mac.dartmouth.edu
- Received by editor(s): July 15, 1994
- Received by editor(s) in revised form: February 23, 1995
- Additional Notes: Supported by DFG–grant Nr. Br 1420/1–1.
- Communicated by: Andreas R. Blass
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2533-2538
- MSC (1991): Primary 03E05, 03E40, 28A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9939-96-03287-X
- MathSciNet review: 1322913