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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]
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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

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References

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