Abstract
AbstractWe 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†.
Publisher
Cambridge University Press (CUP)
Reference6 articles.
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Cited by
3 articles.
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1. A MODEL WITH A PRECIPITOUS IDEAL, BUT NO NORMAL PRECIPITOUS IDEAL;Journal of Mathematical Logic;2013-05-28
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