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How special are Cohen and random forcings, i.e. boolean algebras of the family of subsets of reals modulo meagre or null

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Abstract

We prove that any Souslin c.c.c. forcing notion which adds a nondominated real adds a Cohen real. We also prove that any Souslin c.c.c. forcing adds a real which is not on any old “narrow” tree.

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References

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Author information

Correspondence to Saharon Shelah.

Additional information

Publication 480, partially supported by the Basic Research Fund, Israel Academy of Sciences, and partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany).

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Shelah, S. How special are Cohen and random forcings, i.e. boolean algebras of the family of subsets of reals modulo meagre or null. Israel J. Math. 88, 159–174 (1994). https://doi.org/10.1007/BF02937509

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Keywords

  • Boolean Algebra
  • Random FORCINGS
  • Generic Subset
  • Splitting Node
  • Force Notion