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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.


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

  • Andrzej Nowik (a1) and Tomasz Weiss (a2)
  • DOI:
  • Published online: 01 March 2014

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.

Corresponding author
Polish Academy of Sciences, Institute of Mathematics, Abrahama 18, 81-825 Sopot, Poland, E-mail:
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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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