Fallen cardinals

Menachem Kojman, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We prove that for every singular cardinal μ of cofinality ω, the complete Boolean algebra CompPμ(μ) contains a complete subalgebra which is isomorphic to the collapse algebra CompCol(ω1א0). Consequently, adding a generic filter to the quotient algebra Pμ(μ)=P(μ)/[μ] collapses μא0 to א1. Another corollary is that the Baire number of the space U(μ) of all uniform ultrafilters over μ is equal to ω2. The corollaries affirm two conjectures of Balcar and Simon. The proof uses pcf theory.

Original languageEnglish
Pages (from-to)117-129
Number of pages13
JournalAnnals of Pure and Applied Logic
Issue number1-2
StatePublished - 15 May 2001


  • 03G05
  • 04A10
  • 04A20
  • 54A25
  • 54D80
  • 54F65
  • Baire number
  • Boolean algebra
  • Distributivity
  • Forcing
  • Infinite cardinals
  • Pcf theory
  • Uniform ultrafilters

ASJC Scopus subject areas

  • Logic


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