We answer a question of T. Jech, showing that (1) there may exist weakly precipitous filters inL, and (2) there may exist a weakly precipitous filter on ω1 in a set-generic extension ofL. Hence, the existence of a weakly precipitous filter on ω1 does not imply the existence of 0#.
Winning Strategy Normal Filter Regular Cardinal Elementary Embedding Singular Cardinal
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