Bounded forcing axioms and the continuum

David Asperó, Joan Bagaria

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We show that bounded forcing axioms (for instance, the Bounded Proper Forcing Axiom and the Bounded Semiproper Forcing Axiom) are consistent with the existence of (?,?)-gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level ?, and therefore with the existence of an ?-Suslin tree. We also show that the axiom we call BMM implies ?=?, as well as a stationary reflection principle which has many of the consequences of Martin's Maximum for objects of size ?. Finally, we give an example of a so-called boldface bounded forcing axiom implying 2=?.
Original languageEnglish
Pages (from-to)179-203
Number of pages25
JournalAnnals of Pure and Applied Logic
Volume109
Issue number3
DOIs
Publication statusPublished - 30 May 2001

Keywords

  • Bounded forcing axioms
  • Gaps
  • Open coloring axiom
  • The continuum
  • Boldface bounded forcing axioms

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