Sacks forcing, Laver forcing, and Martin's axiom

Archive for Mathematical Logic 31 (3):145-161 (1992)
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Abstract

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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