Skip to main content
SpringerLink
Log in

MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We prove thatMA(σ-centered) + the Dual Borel Conjecture is consistent; and thatMA(σ-centered) + the non-additivity of the ideal of the strong measure zero sets also is consistent.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Bell,On the combinatorial principle P(c), Fund. Math.134 (1989), 147–149.

    Google Scholar 

  2. T. Bartoszynski,Additivity of measure implies additivity of category, Trans. Am. Math. Soc.281 (1984), 209–213.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Carlson, unpublished notes.

  4. J. Ihoda,Strong measure zero set and rapid filters, J. Symb. Logic53 (1988).

  5. J. Ihoda and S. Shelah,Souslin forming, J. Symb. Logic53 (1988).

  6. K. Kunen,Set Theory, North-Holland, Amsterdam, 1980.

    MATH  Google Scholar 

  7. G. G. Lorentz,On a problem of additive number theory, Proc. Am. Math. Soc.,5 (1954).

  8. D. Martin and R. Solovay,Internal Cohen extensions, Ann. Math. Logic, to appear.

  9. J. Pawlikowski,Powers of transitive bases of measure and category, Proc. Am. Math. Soc.93 (1985), 719–729.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Roitman,Adding a random or a Cohen real: topological consequences and the effect on Martin’s axiom, Fund. Math.C111 (1979), 47–60.

    MathSciNet  Google Scholar 

  11. S. Shelah,Can you take Solovay’s inaccessible away? Isr. J. Math.48 (1984), 1–47.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Haim Judah

  2. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

Authors
  1. Haim Judah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Saharon Shelah
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Jaime Ihoda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Judah, H., Shelah, S. MA(σ-centered): Cohen reals, strong measure zero sets and strongly meager sets. Israel J. Math. 68, 1–17 (1989). https://doi.org/10.1007/BF02764965

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02764965

Keywords

Search

Navigation