Some pathological examples of precipitous ideals
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†.
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2007 ◽
Vol 72
(4)
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pp. 1372-1378
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2001 ◽
Vol 353
(12)
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pp. 4863-4897
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