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Sacks forcing, Laver forcing, and Martin's axiom

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Summary

In this paper we study the question assuming MA+⌝CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals 0. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.

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Authors and Affiliations

  1. Department of Mathematics, Bar-Ilan University, 52900, Ramat-Gan, Israel

    Haim Judah

  2. Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA

    Arnold W. Miller

  3. Institute of Mathematics, Hebrew University, Jerusalem, Israel

    Saharon Shelah

Authors
  1. Haim Judah
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  2. Arnold W. Miller
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  3. Saharon Shelah
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Additional information

Research partially supported by NSF grant 8801139

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Judah, H., Miller, A.W. & Shelah, S. Sacks forcing, Laver forcing, and Martin's axiom. Arch Math Logic 31, 145–161 (1992). https://doi.org/10.1007/BF01269943

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  • DOI: https://doi.org/10.1007/BF01269943

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