Abstract
We prove under the assumption of the existence of a measurable, cardinal and precipitous ideal onw 1 that every Σ 31 set is Lebesgue measurable, has the Baire property and is either countable or contians a perfect subset. We get similar results for Σ 41 sets, if we add the additional assumptions of C. H. and that\(P_w (2^{2w_1 } )\) carries a normal precipitous ideal.
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Magidor, M. Precipitous ideals and Σ 41 setssets. Israel J. Math. 35, 109–134 (1980). https://doi.org/10.1007/BF02760941
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DOI: https://doi.org/10.1007/BF02760941