Israel Journal of Mathematics

, Volume 92, Issue 1–3, pp 349–359 | Cite as

No random reals in countable support iterations

  • Haim Judah
  • Miroslav Repický


We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals.


Inverse Limit Random Real Force Notion Baire Space Majorant Series 
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. [1]
    T. Bartoszynski,Additivity of measure implies additivity of category, Transactions of the American Mathematical Society281 (1984), 209–213.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    T. Bartoszynski and H. Judah,Measure and Category, in preparation.Google Scholar
  3. [3]
    T. Bartoszynski and H. Judah,Jumping with random reals, Annals of Pure and Applied Logic48 (1990), 197–213.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    M. Goldstern,Forcing tools for your forcing construction, inSet Theory of the Reals 1991 (H. Judah, ed.), Israel Mathematical Conference Proceeding6 (1993), 305–360.Google Scholar
  5. [5]
    T. Jech,Set Theory, Academic Press, New York, 1978.Google Scholar
  6. [6]
    A.W. Miller,Some properties of measure and category, Transactions of the American Mathematical Society266 (1981), 93–114.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    J. Pawlikowski,Why Solovay real produces Cohen real, Journal of Symbolic Logic51 (1986), 957–968.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    J. Raisonnier and J. Stern,The strength of measurability hypothesis, Israel Journal of Mathematics50 (1985), 337–349.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    S. Shelah,Proper Forcing, Lecture Notes in Mathematics940, Spring-Verlag, Berlin, 1982.zbMATHGoogle Scholar
  10. [10]
    S. Shelah,Proper and Improper Forcing, to appear.Google Scholar
  11. [11]
    J. Stern,Generic extensions which do not add random reals, Proc. Caracas, Lecture Notes in Mathematics1130, Springer-Verlag, Berlin, 1983, pp. 395–407.Google Scholar

Copyright information

© Hebrew University 1995

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceBar Ilan UniversityRamat GanIsrael
  2. 2.Matematický ústav SAVKošiceSlovakia

Personalised recommendations