Archive for Mathematical Logic

, Volume 31, Issue 3, pp 145–161

Sacks forcing, Laver forcing, and Martin's axiom

  • Haim Judah
  • Arnold W. Miller
  • Saharon Shelah

DOI: 10.1007/BF01269943

Cite this article as:
Judah, H., Miller, A.W. & Shelah, S. Arch Math Logic (1992) 31: 145. doi:10.1007/BF01269943


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 ideals0. 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.

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Haim Judah
    • 1
  • Arnold W. Miller
    • 2
  • Saharon Shelah
    • 3
  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA
  3. 3.Institute of MathematicsHebrew UniversityJerusalemIsrael

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