Depth of boolean algebras

Shimon Garti*, Saharon Shela

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Suppose D is an ultrafilter on κ and λκ = λ. We prove that if Bi is a Boolean algebra for every i < κ and λ bounds the depth of every Bi , then the depth of the ultraproduct of the Bi 's mod D is bounded by λ+. We also show that for singular cardinals with small cofinality, there is no gap at all. This gives a partial answer to a previous problem raised by Monk.

Original languageAmerican English
Pages (from-to)307-314
Number of pages8
JournalNotre Dame Journal of Formal Logic
Volume52
Issue number3
DOIs
StatePublished - 2011

Keywords

  • Boolean algebras
  • Constructability
  • Depth

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