Israel Journal of Mathematics

, Volume 92, Issue 1–3, pp 349–359

No random reals in countable support iterations



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.


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Copyright information

© Hebrew University 1995

Authors and Affiliations

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

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