On almost precipitous ideals

Asaf Ferber, Moti Gitik*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


With less than 0# two generic extensions of L are identified: one in which א1, and the other א2, is almost precipitous. This improves the consistency strength upper bound of almost precipitousness obtained in Gitik M, Magidor M (On partialy wellfounded generic ultrapowers, in Pillars of Computer Science, 2010), and answers some questions raised there. Also, main results of Gitik (On normal precipitous ideals, 2010), are generalized-assumptions on precipitousness are replaced by those on ∞-semi precipitousness. As an application it is shown that if δ is a Woodin cardinal and there is an f: ω1 → ω2 with {double pipe}f{double pipe} = ω2, then after Col(א2, δ) there is a normal precipitous ideal over א1. The existence of a pseudo-precipitous ideal over a successor cardinal is shown to give an inner model with a strong cardinal.

Original languageEnglish
Pages (from-to)301-328
Number of pages28
JournalArchive for Mathematical Logic
Issue number3
StatePublished - 2010


  • Almost precipitous ideals
  • Generic ultrapowers
  • Well foundedness


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