Nowik, Andrzej; Weiss, Tomasz Strongly meager sets of real numbers and tree forcing notions. (English) Zbl 0996.03030 Proc. Am. Math. Soc. 130, No. 4, 1183-1187 (2002). 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. \(l_0\)-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 \(2^\omega\). J. Brendle [Fundam. Math. 148, 1-25 (1995; Zbl 0835.03010)] has shown that neither of these two classes is included in the other. Reviewer: Alberto Marcone (Udine) Cited in 1 ReviewCited in 1 Document MSC: 03E15 Descriptive set theory 03E20 Other classical set theory (including functions, relations, and set algebra) 28E15 Other connections with logic and set theory Keywords:strongly meager set; Laver forcing; Miller forcing Citations:Zbl 0835.03010 PDFBibTeX XMLCite \textit{A. Nowik} and \textit{T. Weiss}, Proc. Am. Math. Soc. 130, No. 4, 1183--1187 (2002; Zbl 0996.03030) Full Text: DOI References: [1] Jörg Brendle, Strolling through paradise, Fund. Math. 148 (1995), no. 1, 1 – 25. · Zbl 0835.03010 [2] G.G. Lorentz, On a problem of additive number theory, Proceedings of the American Mathematical Society 5 (1954), 838 - 841. · Zbl 0056.03902 [3] Andrzej Nowik and Tomasz Weiss, Strongly meager sets and their uniformly continuous images, Proc. Amer. Math. Soc. 129 (2001), no. 1, 265 – 270. · Zbl 0955.03050 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.