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    Bartoszynski, Tomek Nowik, Andrzej and Weiss, Tomasz 2004. Strongly meager sets can be quite big. Israel Journal of Mathematics, Vol. 139, Issue. 1, p. 237.


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On the Ramseyan properties of some special subsets of 2ω and their algebraic sums

  • Andrzej Nowik (a1) and Tomasz Weiss (a2)
  • DOI: http://dx.doi.org/10.2178/jsl/1190150097
  • Published online: 01 March 2014
Abstract
Abstract

We prove the following theorems:

1. If X ⊆ 2ω is a γ-set and Y ⊆2ω is a strongly meager set, then X + Y is Ramsey null.

2. If X ⊆2ω is a γ-set and Y belongs to the class of sets, then the algebraic sum X + Y is an set as well.

3. Under CH there exists a set XMGR* which is not Ramsey null.

Copyright
Corresponding author
Polish Academy of Sciences, Institute of Mathematics, Abrahama 18, 81-825 Sopot, Poland, E-mail: nowik@impan.gda.pl
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[5]A. Nowik and T. Weiss , Strongly meager sets and their uniformly continuous images, Proceedings of the American Mathematical Society, vol. 129, no. 1, pp. 265270.

[6]J. Pawlikowski , A characterization of strong measure zero sets, Israel Journal of Mathematics, vol. 93 (1996), pp. 161194.

[8]S. Shelah , Every null additive set is meagre additive, Israel Journal of Mathematics, vol. 89 (1995), pp. 357376.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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