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June 2008 Some pathological examples of precipitous ideals
Moti Gitik
J. Symbolic Logic 73(2): 492-511 (June 2008). DOI: 10.2178/jsl/1208359056

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.

Citation

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Moti Gitik. "Some pathological examples of precipitous ideals." J. Symbolic Logic 73 (2) 492 - 511, June 2008. https://doi.org/10.2178/jsl/1208359056

Information

Published: June 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1140.03032
MathSciNet: MR2414461
Digital Object Identifier: 10.2178/jsl/1208359056

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 2 • June 2008
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