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Special subsets of the reals and tree forcing notions
Authors:Marcin Kysiak   Andrzej Nowik   Tomasz Weiss
Affiliation:Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland ; Institute of Mathematics, University of Gdansk, Wita Stwosza 57, 80-952 Gdansk, Poland ; Institute of Mathematics and Physics, Akademia Podlaska, ul. 3-go Maja, 08-110 Siedlce, Poland
Abstract: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.

Keywords:$gamma$-set   Rothberger's property   meager-additive set   $sigma$-set   Laver forcing   Miller forcing   Silver forcing   completely Ramsey-null set
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