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Special subsets of the reals and tree forcing notions
Author(s):
Marcin
Kysiak;
Andrzej
Nowik;
Tomasz
Weiss
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2975-2982.
MSC (2000):
Primary 03E05, 03E35, 28E15, 54G99
Posted:
May 9, 2007
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Additional information
Abstract:
We study relationships between classes of special subsets of the reals (e.g. meager-additive sets,  -sets,  -sets,  -sets) and the ideals related to the forcing notions of Laver, Mathias, Miller and Silver.
References:
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- 6.
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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 Gdansk, Wita Stwosza 57, 80-952 Gdansk, 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:
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
Posted:
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
Copyright of article:
Copyright
2007,
American Mathematical Society
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