# Sh:781

• Kojman, M., & Shelah, S. (2003). van der Waerden spaces and Hindman spaces are not the same. Proc. Amer. Math. Soc., 131(5), 1619–1622.
• Abstract:
A Hausdorff topological space X is van der Waerden if for every sequence (x_n)_n in X there is a converging subsequence (x_n)_{n\in A} where A\subseteq\omega contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (x_n)_n in X there is an IP-converging subsequence (x_n)_{n\in FS(B)} for some infinite B\subseteq\omega. We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.
• Current version: 2001-11-20_11 (4p) published version (4p)
Bib entry
@article{Sh:781,
author = {Kojman, Menachem and Shelah, Saharon},
title = {{van der Waerden spaces and Hindman spaces are not the same}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {131},
number = {5},
year = {2003},
pages = {1619--1622},
issn = {0002-9939},
mrnumber = {1950294},
mrclass = {54A20 (03E35 03E50)},
doi = {10.1090/S0002-9939-02-06916-2},
note = {\href{https://arxiv.org/abs/math/0112265}{arXiv: math/0112265}},
arxiv_number = {math/0112265}
}