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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Special subsets of the reals and tree forcing notions


Authors: Marcin Kysiak, Andrzej Nowik and Tomasz Weiss
Journal: Proc. Amer. Math. Soc. 135 (2007), 2975-2982
MSC (2000): Primary 03E05, 03E35, 28E15, 54G99
Published electronically: May 9, 2007
MathSciNet review: 2317976
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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.


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Additional Information

Marcin Kysiak
Affiliation: Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
Email: mkysiak@mimuw.edu.pl

Andrzej Nowik
Affiliation: Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Email: nowik@math.uni.gda.pl

Tomasz Weiss
Affiliation: Institute of Mathematics and Physics, Akademia Podlaska, ul. 3-go Maja, 08-110 Siedlce, Poland
Email: tomaszweiss@o2.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08808-9
PII: S 0002-9939(07)08808-9
Keywords: $\gamma$-set, Rothberger's property, meager-additive set, $\sigma$-set, Laver forcing, Miller forcing, Silver forcing, completely Ramsey-null set
Received by editor(s): March 13, 2006
Received by editor(s) in revised form: June 8, 2006
Published electronically: May 9, 2007
Additional Notes: A part of the research was made when the first author was visiting the Institute of Mathematics of the Polish Academy of Sciences
The second author was partially supported by grant BW/5100-5-0201-6
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society