Strongly meager sets of real numbers and tree forcing notions (Q2781269)

In this paper the authors prove that every strongly meager subset of \(2^\omega\) is both an \(l_0\)-set and an \(m_0\)-set. NEWLINENEWLINENEWLINE\(l_0\)-sets and \(m_0\)-sets are notions of smallness related, respectively, to Laver and Miller forcing and are best viewed as subsets of \([\omega]^\omega\), which is naturally identified with a \(G_\delta\) subset of \(2^\omega\). \textit{J. Brendle} [Fundam. Math. 148, 1-25 (1995; Zbl 0835.03010)] has shown that neither of these two classes is included in the other.