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 | References | Similar Articles | 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.

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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

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