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Mathematica Slovaca

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Volume 68, Issue 3


Small-large subgroups of the reals

Andrzej Rosłanowski / Saharon Shelah
  • Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem Israel
  • Department of Mathematics Rutgers University New Brunswick NJ 08854 USA
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Published Online: 2018-05-18 | DOI: https://doi.org/10.1515/ms-2017-0117


We are interested in subgroups of the reals that are small in one and large in another sense. We prove that, in ZFC, there exists a non-meager Lebesgue null subgroup of ℝ, while it is consistent that there there is no non-null meager subgroup of ℝ.

MSC 2010: Primary 03E35; Secondary: 28A05, 54A05

Keywords: null ideal; meager ideal; additive subgroups of the reals; Borel hulls; forcing


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About the article

Both authors acknowledge support from the United States-Israel Binational Science Foundation (Grant no. 2010405). Publication 1081 of the second author.

URL: http://www.math.rutgers.edu/∼shelah


Received: 2016-06-04

Accepted: 2016-10-12

Published Online: 2018-05-18

Published in Print: 2018-06-26

Citation Information: Mathematica Slovaca, Volume 68, Issue 3, Pages 473–484, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0117.

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