Depth+ and length+ of boolean algebras

Shimon Garti, Saharon Shelah

Research output: Contribution to journalArticlepeer-review


Suppose that κ = cf(κ), λ > cf(λ) = κ+ and λ = λκ. We prove that there exist a sequence hBi : i < κi of Boolean algebras and an ultrafilter D over κ so that λ = Q Depth+(Bi)/D < Depth+(Q Bi/D) = λ+. An i<κ i<κ identical result holds also for Length+. The proof is carried in ZFC, and it holds even above large cardinals.

Original languageAmerican English
Pages (from-to)953-963
Number of pages11
JournalHouston Journal of Mathematics
Issue number4
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 University of Houston


  • Boolean algebras
  • Depth
  • Ultraproducts


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