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Small subsets of the reals and tree forcing notions
Author(s):
Marcin
Kysiak;
Tomasz
Weiss
Journal:
Proc. Amer. Math. Soc.
132
(2004),
251-259.
MSC (2000):
Primary 03E35, 28E15
Posted:
May 28, 2003
MathSciNet review:
2021269
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Abstract:
We discuss the question of which properties of smallness in the sense of measure and category (e.g. being a universally null, perfectly meager or strongly null set) imply the properties of smallness related to some tree forcing notions (e.g. the properties of being Laver-null or Miller-null).
References:
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Additional Information:
Marcin
Kysiak
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warszawa, Poland
Email:
mkysiak@impan.gov.pl
Tomasz
Weiss
Affiliation:
Institute of Mathematics, WSRP, 08-110 Siedlce, Poland
Email:
weiss@wsrp.siedlce.pl
DOI:
10.1090/S0002-9939-03-07026-6
PII:
S 0002-9939(03)07026-6
Keywords:
Perfectly meager set,
universally null set,
strong measure zero set,
Laver forcing,
Miller forcing
Received by editor(s):
June 11, 2002
Received by editor(s) in revised form:
September 3, 2002
Posted:
May 28, 2003
Additional Notes:
The first author is a Ph.D. student at the Institute of Mathematics of the Polish Academy of Sciences. A part of this work is likely to be included in his doctorate written under the supervision of P. Zakrzewski
Communicated by:
Carl G. Jockusch, Jr.
Copyright of article:
Copyright
2003,
American Mathematical Society
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