Ladder gaps over stationary sets

Uri Abraham, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


For a stationary set S ⊆ ω1 and A ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over ω1 / S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c. posets is again a polarized c.c.c. poset.

Original languageEnglish
Pages (from-to)518-532
Number of pages15
JournalJournal of Symbolic Logic
Issue number2
StatePublished - 1 Jun 2004

ASJC Scopus subject areas

  • Philosophy
  • Logic


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