There are no very meager sets in the model in which both the Borel Conjecture and the dual Borel Conjecture are true

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Mathematical Logic Quarterly 62 (4-5):434-438 (2016)
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Abstract

We show that the model for the simultaneous consistency of the Borel Conjecture and the dual Borel Conjecture given in actually satisfies a stronger version of the dual Borel Conjecture: there are no uncountable very meager sets.

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10.1002/malq.201600002

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Strongly Meager Sets Do Not Form an Ideal.Tomek Bartoszynski & Saharon Shelah - 2001 - Journal of Mathematical Logic 1 (1):1-34.

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