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Lifting problem of the measure algebra

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Abstract

We prove the consistency of “ℬ/I mz does not split” (see Notation). We write the proof so that with the standard duality, also the consistency of “ℬ/I tc does not split” (i.e., replacing measure zero by first category, random by generic, etc.) is proved. The method is the oracle chain condition.

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References

  1. T. Jech,Set Theory, Academic Press, 1976.

  2. J. C. Oxtoby,Measure and Category Theory, Springer-Verlag, 1971.

  3. S. Shelah,Independence results, J. Symp. Logic45 (1980), 563–573.

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  4. S. Shelah,Proper Forcing, Lecture Notes in Math.940, Springer-Verlag, 1982.

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Authors and Affiliations

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

    Saharon Shelah

  2. Institute for Advanced Studies, The Hebrew University of Jerusalem, Jerusalem, Israel

    Saharon Shelah

  3. Department of Mathematics, University of California, Berkeley, California, USA

    Saharon Shelah

Authors
  1. Saharon Shelah
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Additional information

The author would like to thank the NSF and BSF (United States-Israel Binational Science Foundation) for partially supporting this research.

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Shelah, S. Lifting problem of the measure algebra. Israel J. Math. 45, 90–96 (1983). https://doi.org/10.1007/BF02760673

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  • DOI: https://doi.org/10.1007/BF02760673

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