Density versions of Schur's theorem for ideals generated by submeasures

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:117

Article

Filipow, Rafal¹  Szuca, Piotr¹ 

[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

关键词: Bolzano-Weierstrass theorem;    Bolzano-Weierstrass property;    Ideal convergence;    Statistical density;    Statistical convergence;    Subsequence;    Schur's theorem;   

DOI  :  10.1016/j.jcta.2009.12.005

来源: Elsevier

【 摘 要 】

We characterize ideals of subsets of natural numbers for which some versions of Schur's theorem hold. These are similar to generalizations shown by Bergelson (1986) in [1] and Frankl, Graham and Rodl (1990) in [7]. Additionally, we prove a generalization of an iterated version of Ramsey's theorem. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free