Abstract
We consider a question of T. Jech and K. Prikry that asks if the existence of a precipitous filter implies the existence of a normal precipitous filter. The aim of this paper is to improve a result of Gitik (Israel J Math, 175:191-219, 2010) and to show that measurable cardinals of a higher order rather than just measurable cardinals are necessary in order to have a model with a precipitous filter but without a normal one.
Original language | English |
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Pages (from-to) | 223-243 |
Number of pages | 21 |
Journal | Archive for Mathematical Logic |
Volume | 50 |
Issue number | 1-2 |
DOIs | |
State | Published - Feb 2011 |
Keywords
- Generic ultrapowers
- Precipitous ideals
- Well foundedness