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No random reals in countable support iterations

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Bar Ilan University, 52900, Ramat Gan, Israel

    Haim Judah

  2. Matematický ústav SAV, Jesenná 5, 041 54, Košice, Slovakia

    Miroslav Repický

Authors
  1. Haim Judah
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  2. Miroslav Repický
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Corresponding author

Correspondence to Haim Judah.

Additional information

The work was supported by BRF of Israel Academy of Sciences and by grant GA SAV 365 of Slovak Academy of Sciences.

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Judah, H., Repický, M. No random reals in countable support iterations. Israel J. Math. 92, 349–359 (1995). https://doi.org/10.1007/BF02762088

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  • DOI: https://doi.org/10.1007/BF02762088

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