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Strongly meager sets of real numbers and tree forcing notions. (English) Zbl 0996.03030

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.

MSC:

03E15 Descriptive set theory
03E20 Other classical set theory (including functions, relations, and set algebra)
28E15 Other connections with logic and set theory

Citations:

Zbl 0835.03010
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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
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