Starting with a measurable cardinal κ of the Mitchell order κ++ we construct a model with a precipitous ideal on N 1 but without normal precipitous ideals. This answers a question by T. Jech and K. Prikry. In the constructed model there are no Q-point precipitous filters on N1, i. e. those isomorphic to extensions of Cub N1.
- Precipitous ideals
- Rudin-Keisler increasing sequences
- ∞-semi precipitous filters