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. arXiv: math/0112265 DOI: 10.1090/S0002-9939-02-06916-2 MR: 1950294
• 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.
• Version 2001-11-20_11 (4p) published version (4p)

@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}
}