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Strongly meager sets of size continuum

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Abstract.

We will construct several models where there are no strongly meager sets of size 2ℵ0.

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References

  1. Bartoszynski, T., Judah, H.: Set Theory: on the structure of the real line. A.K. Peters, 1995

  2. Bartoszynski, T., Shelah, S.: Strongly meager sets do not form an ideal. J. Math. Logic 1, 1–34 (2001)

    Article  MathSciNet  Google Scholar 

  3. Borel, E.: Sur la classification des ensembles de mesure nulle. Bulletin de la Societe Mathematique de France 47, 97–125 (1919)

    MATH  Google Scholar 

  4. Carlson, T.J.: Strong measure zero and strongly meager sets. Proc. Amer. Math. Soc. 118(2), 577–586 (1993)

    MATH  Google Scholar 

  5. Eisworth, T.: Contributions to the theory of proper forcing. Ph.D. thesis, 1994

  6. Erdos, P., Kunen, K., Mauldin, R.D.: Some additive properties of sets of real numbers. Fundamenta Mathematicae 113(3), 187–199 (1981)

    Google Scholar 

  7. Galvin, F., Mycielski, J., Solovay, R.: Strong measure zero sets. Notices Amer. Math. Soc. pages A–280, 1973

  8. Goldstern, M.: Tools for your forcing constructions. In Haim Judah, editor, Set theory of the reals, Israel Mathematical Conference Proceedings, pages 305–360. Bar Ilan University, 1992

  9. Goldstern, M., Judah, H., Shelah., S.: Strong measure zero sets without Cohen reals. J. Symbolic Logic 58(4), 1323–1341 (1993)

    MATH  Google Scholar 

  10. Kysiak, M.: Master’s Thesis, Warsaw University. In Polish, 2000

  11. Nowik, A., Weiss, T.: Strongly meager sets of real numbers and tree forcing notions. Proc. Amer. Math. Soc. 130(4), 1183–1187 (2002)

    Article  MATH  Google Scholar 

  12. Pawlikowski, J.: Why Solovay real produces Cohen real. J. Symbolic Logic 51(4), 957–968 (1986)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Boise State University, Boise, Idaho, 83725, USA

    Tomek Bartoszynski

  2. Department of Mathematics, Hebrew University, Jerusalem, Israel

    Saharon Shelah

  3. Department of Mathematics, Rutgers University, New Brunswick, NJ, USA

    Saharon Shelah

Authors
  1. Tomek Bartoszynski
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  2. Saharon Shelah
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Corresponding author

Correspondence to Tomek Bartoszynski.

Additional information

First author partially supported by NSF grant DMS 0200671.

Second author partially supported by Israel Science Foundation and NSF grant DMS 0072560. Publication 807.

Mathematics Subject Classification (2000): 03E15, 03E20

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Bartoszynski, T., Shelah, S. Strongly meager sets of size continuum. Arch. Math. Logic 42, 769–779 (2003). https://doi.org/10.1007/s00153-003-0184-0

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  • DOI: https://doi.org/10.1007/s00153-003-0184-0

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