Projective absoluteness for Sacks forcing

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Abstract

We show that ∑1/3-absoluteness for Sacks forcing is equivalent to the non-existence δ1/2 of a Bernstein set. We also show that Sacks forcing is the weakest forcing notion among all of the preorders that add a new real with respect to ∑1/3 forcing absoluteness.

Original languageEnglish
Pages (from-to)679-690
Number of pages12
JournalArchive for Mathematical Logic
Volume48
Issue number7
DOIs
Publication statusPublished - 2009 Sep
Externally publishedYes

Keywords

  • Bernstein sets
  • Forcing absoluteness
  • Sacks forcing

ASJC Scopus subject areas

  • Philosophy
  • Logic

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