On the strength of no normal precipitous filter

Moti Gitik*, Liad Tal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191-219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.

Original languageEnglish
Pages (from-to)223-243
Number of pages21
JournalArchive for Mathematical Logic
Issue number1-2
StatePublished - Feb 2011


  • Generic ultrapowers
  • Precipitous ideals
  • Well foundedness


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