Sacks forcing, Laver forcing, and Martin's axiom

Haim Judah; Arnold W. Miller; Saharon Shelah

doi:10.1007/BF01269943

Sacks forcing, Laver forcing, and Martin's axiom

Haim Judah^*
, Arnold W. Miller
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

In this paper we study the question assuming MA+{top right corner}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 ideal s⁰. 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.

Original language	English
Pages (from-to)	145-161
Number of pages	17
Journal	Archive for Mathematical Logic
Volume	31
Issue number	3
DOIs	https://doi.org/10.1007/BF01269943
State	Published - May 1992

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abstract = "In this paper we study the question assuming MA+\{top right corner\}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 ideal s0. 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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AB - In this paper we study the question assuming MA+{top right corner}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 ideal s0. 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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Sacks forcing, Laver forcing, and Martin's axiom

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