The Journal of Symbolic Logic

Research Article

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

Andrzej Nowika1 c1 and Tomasz Weissa2

a1 University of Gdańsk, Institute of Mathematics, Wita Stwosza 57, 80-952 Gdańsk, Poland, E-mail: matan@paula.univ.gda.pl

a2 Institute of Mathematics, WSRP, 08-110 Siedlce, Poland, E-mail: weiss@wsrp.siedlce.pl

Abstract

We prove the following theorems:

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

2. If X ⊆2 ω 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.

(Received October 02 1999)

(Revised February 23 2001)

Key words and phrases

  • Strongly meager sets;
  • Ramsey null sets;
  • (T') sets

Correspondence

c1 Polish Academy of Sciences, Institute of Mathematics, Abrahama 18, 81-825 Sopot, Poland, E-mail: nowik@impan.gda.pl

Footnotes

  Partially supported by the KBN grant 2 P03A 047 09.