Mad families and non-meager filters

by Horowitz and Shelah. [HwSh:1103]

We prove the consistency of ZF + DC + ``there are no mad families'' + ``there exists a non-meager filter on omega'' relative to ZFC, answering a question of Neeman and Norwood. We also introduce a weaker version of madness, and we strengthen the result from [HwSh:1090] by showing that no such families exist in our model.

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