Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-06T10:02:17.970Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  12 March 2014

Andrzej Nowik  and
Tomasz Weiss
Andrzej Nowik*
Affiliation:
University of Gdańsk, Institute of Mathematics, Wita Stwosza 57, 80-952 Gdańsk, Poland, E-mail: [email protected]
Tomasz Weiss
Affiliation:
Institute of Mathematics, WSRP, 08-110 Siedlce, Poland, E-mail: [email protected]
*
Polish Academy of Sciences, Institute of Mathematics, Abrahama 18, 81-825 Sopot, Poland, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 X ∈ MGR* which is not Ramsey null.

Keywords

Strongly meager setsRamsey null sets(T') sets
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 547 - 556
Copyright
Copyright © Association for Symbolic Logic 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bartoszyński, T. and Judah, H., Set Theory, A.K. Peters, Wellesley, Massachusetts, 1995.CrossRefGoogle Scholar
[2]Brown, J., The Ramsey sets and related Sigma algebras and ideals, Fundamenta Mathematicae, vol. 136 (1990), pp. 179–185.CrossRefGoogle Scholar
[3]Brown, J. B. and Cox, G. V., Classical theory of totally imperfect spaces, Real Analysis Exchange, vol. 7 (1981–1982), pp. 185–232.CrossRefGoogle Scholar
[4]Nowik, A., Scheepers, M., and Weiss, T., The algebraic sum of sets of real numbers with strong measure zero sets, this Journal, vol. 63 (1998), no. 1, pp. 301–324.Google Scholar
[5]Nowik, A. and Weiss, T., Strongly meager sets and their uniformly continuous images, Proceedings of the American Mathematical Society, vol. 129, no. 1, pp. 265–270.CrossRefGoogle Scholar
[6]Pawlikowski, J., A characterization of strong measure zero sets, Israel Journal of Mathematics, vol. 93 (1996), pp. 161–194.CrossRefGoogle Scholar
[7]Pawlikowski, J. and Recław, I., Parametrized Cichoń's diagram and small sets, Fundamenta Mathematicae, vol. 147 (1995), pp. 135–155.CrossRefGoogle Scholar
[8]Shelah, S., Every null additive set is meagre additive, Israel Journal of Mathematics, vol. 89 (1995), pp. 357–376.CrossRefGoogle Scholar
[9]Talagrand, M., Sommes vectorielles dçensembles de mesure nulle, Comptes Rendus de l' Académie des Sciences, Paris, vol. 280 (1975), pp. 853–855.Google Scholar