Baumgartner's conjecture and bounded forcing axioms

David Asperó, Sy-David Friedman, Miguel Angel Mota, Marcin Sabok

Research output: Contribution to journalArticle

Abstract

We study the spectrum of forcing notions between the iterations of s-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of a-proper forcings for indecomposable countable ordinals a, the Axiom A forcings and forcings completely embeddable into an iteration of a s-closed followed by a ccc forcing. For the latter class, we present an equivalent characterization in terms of Baumgartner's Axiom A. This resolves a conjecture of Baumgartner from the 1980s. We also study the bounded forcing axioms for the hierarchy of a-proper forcings. Following ideas of Shelah we separate them for distinct countable indecomposable ordinals.
Original languageEnglish
Pages (from-to)1178-1786
Number of pages609
JournalAnnals of Pure and Applied Logic
Volume164
Issue number12
DOIs
Publication statusPublished - 1 Dec 2013

Keywords

  • Proper forcing
  • Axiom A forcing
  • Bounded forcing axioms

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