TY - JOUR
T1 - A model with a precipitous ideal, but no normal precipitous ideal
AU - Gitik, Moti
N1 - Funding Information:
We are grateful to the referee of the paper for his suggestions as well as for a long and comprehensive list of corrections. This work was partially supported by ISF Grant 234/08.
PY - 2013/6
Y1 - 2013/6
N2 - 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.
AB - 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.
KW - Precipitous ideals
KW - Rudin-Keisler increasing sequences
KW - normality
KW - ∞-semi precipitous filters
UR - https://www.scopus.com/pages/publications/84878457373
U2 - 10.1142/S0219061312500080
DO - 10.1142/S0219061312500080
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AN - SCOPUS:84878457373
SN - 0219-0613
VL - 13
JO - Journal of Mathematical Logic
JF - Journal of Mathematical Logic
IS - 1
M1 - 1250008
ER -