Geodesic
A note on the intersection ideal $\mathcal M\cap \mathcal N$
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 437-445

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We prove among other theorems that it is consistent with $ZFC$ that there exists a set $X\subseteq 2^\omega$ which is not meager additive, yet it satisfies the following property: for each $F_\sigma$ measure zero set $F$, $X+F$ belongs to the intersection ideal $\mathcal M\cap \mathcal N$.
Classification : 03E05, 03E17
Keywords: $F_\sigma$ measure zero sets; intersection ideal $\mathcal M\cap \mathcal N$; meager additive sets; sets perfectly meager in the transitive sense; $\gamma$-sets 
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     title = {A note on the intersection ideal $\mathcal M\cap \mathcal N$},
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Weiss, Tomasz. A note on the intersection ideal $\mathcal M\cap \mathcal N$. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 3, pp. 437-445. http://geodesic.mathdoc.fr/item/CMUC_2013__54_3_a9/