## Tomasz Weiss

*A note on the intersection ideal $\mathcal M\cap \mathcal N$*

Comment.Math.Univ.Carolin. 54,3 (2013) 437-445.**Abstract:**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 $\mathcal M\cap \mathcal N$.

**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

**AMS Subject Classification:** 03E05 03E17

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