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

 

Small subsets of the reals and tree forcing notions


Authors: Marcin Kysiak and Tomasz Weiss
Journal: Proc. Amer. Math. Soc. 132 (2004), 251-259
MSC (2000): Primary 03E35, 28E15
Published electronically: 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).


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Additional Information

Marcin Kysiak
Affiliation: Institute of Mathematics of the Polish Academy of Sciences, ul. Śniadeckich 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: http://dx.doi.org/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
Published electronically: 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.
Article copyright: © Copyright 2003 American Mathematical Society