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Mathematica Slovaca

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Volume 68, Issue 3

Issues

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

Abstract

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

References

  • [1]

    Bartoszyński, T.—judah, H.: Set Theory: On the Structure of the Real Line, A K Peters, Wellesley, Massachusetts, 1995.Google Scholar

  • [2]

    Baumgartner, J. E.: Iterated forcing. In: Surveys in Set Theory (A. Mathias, ed.), London Math. Soc. Lecture Note Ser. 87, Cambridge, Britain, pp. 1–59.Google Scholar

  • [3]

    Baumgartner, J. E.: Sacks forcing and the total failure of Martin’s axiom, Topology Appl. 19 (1985), 211–225.CrossrefGoogle Scholar

  • [4]

    Bukovský, L.: The Structure of the Real Line. Monogr. Mat. 71, Birkhäuser, 2011.Google Scholar

  • [5]

    Filipczak, T.—Rosłanowski, A.—Shelah, S.: On Borel hull operations, Real Anal. Exchange 40 (2015), 129–140. arxiv:1308.3749CrossrefGoogle Scholar

  • [6]

    Jech, T.: Set Theory. Springer Monogr. Math., Springer-Verlag, Berlin, 2003. The third millennium edition, revised and expanded.Google Scholar

  • [7]

    Rosłanowski,, A.: n-localization property, J. Symbolic Logic 71 (2006), 881–902. arxiv:math.LO/0507519.CrossrefGoogle Scholar

  • [8]

    Rosłanowski, A.—Shelah, S.: Norms on possibilities I: forcing with trees and creatures. Mem. Amer. Math. Soc. 141(671), 1999. arxiv:math.LO/9807172.Google Scholar

  • [9]

    Rosłanowski, A.—Steprāns J.: Chasing Silver. Canad. Math. Bull. 51 (2008), 593–603. arxiv:math.LO/0509392CrossrefGoogle Scholar

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

*1

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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