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Special subsets of the reals and tree forcing notions. (English) Zbl 1121.03056

Summary: Continuing our earlier papers [A. Nowik and T. Weiss, Proc. Am. Math. Soc. 130, 1183–1187 (2002; Zbl 0996.03030); M. Kysiak and T. Weiss, ibid. 132, 251–259 (2004; Zbl 1035.03026)], we study relationships between classes of special subsets of the reals (e.g. meager-additive sets, \( \gamma\)-sets, \( C''\)-sets, \( \lambda\)-sets) and the ideals related to the forcing notions of Laver, Mathias, Miller and Silver.

MSC:

03E05 Other combinatorial set theory
03E35 Consistency and independence results
28E15 Other connections with logic and set theory
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