Some pathological examples of precipitous ideals

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Abstract

We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [2] and R. Laver [4] respectively. The present examples differ in two ways: first- they use only a measurable cardinal and second- the ideals are over a cardinal. Also a precipitous ideal without a normal ideal below it is constructed. It is shown in addition that if there is a precipitous ideal over a cardinal κ such that after the forcing with its positive sets the cardinality of κ remains above א1 there is no a normal precipitous ideal then there is 0†.

Original languageEnglish
Pages (from-to)492-511
Number of pages20
JournalJournal of Symbolic Logic
Volume73
Issue number2
DOIs
StatePublished - Jun 2008

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