Some pathological examples of precipitous ideals

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 [1] 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 such that

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: Moti Gitik
• Keywords: Indecisive Precipitous Ideal, JSYML 2008, Normal Ideal, Precipitous Ideal