Israel Journal of Mathematics

, Volume 68, Issue 1, pp 1–17 | Cite as

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

  • Haim Judah
  • Saharon Shelah


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.


Finite Union Random Real Strong Measure Force Notion Finite Support 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 0.
    M. Bell,On the combinatorial principle P(c), Fund. Math.134 (1989), 147–149.Google Scholar
  2. 1.
    T. Bartoszynski,Additivity of measure implies additivity of category, Trans. Am. Math. Soc.281 (1984), 209–213.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 2.
    T. Carlson, unpublished notes.Google Scholar
  4. 3.
    J. Ihoda,Strong measure zero set and rapid filters, J. Symb. Logic53 (1988).Google Scholar
  5. 4.
    J. Ihoda and S. Shelah,Souslin forming, J. Symb. Logic53 (1988).Google Scholar
  6. 5.
    K. Kunen,Set Theory, North-Holland, Amsterdam, 1980.zbMATHGoogle Scholar
  7. 6.
    G. G. Lorentz,On a problem of additive number theory, Proc. Am. Math. Soc.,5 (1954).Google Scholar
  8. 7.
    D. Martin and R. Solovay,Internal Cohen extensions, Ann. Math. Logic, to appear.Google Scholar
  9. 8.
    J. Pawlikowski,Powers of transitive bases of measure and category, Proc. Am. Math. Soc.93 (1985), 719–729.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 9.
    J. Roitman,Adding a random or a Cohen real: topological consequences and the effect on Martin’s axiom, Fund. Math.C111 (1979), 47–60.MathSciNetGoogle Scholar
  11. 10.
    S. Shelah,Can you take Solovay’s inaccessible away? Isr. J. Math.48 (1984), 1–47.zbMATHCrossRefGoogle Scholar

Copyright information

© Hebrew University 1989

Authors and Affiliations

  • Haim Judah
    • 1
  • Saharon Shelah
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations